ORCID Profile
0000-0001-6477-1419
Current Organisation
University of Tasmania
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Publisher: Elsevier BV
Date: 02-1993
Publisher: IOP Publishing
Date: 03-1981
Publisher: Springer Science and Business Media LLC
Date: 10-1970
DOI: 10.1007/BF02726481
Publisher: Elsevier BV
Date: 07-1972
Publisher: American Physical Society (APS)
Date: 15-08-1982
Publisher: American Physical Society (APS)
Date: 06-1994
Publisher: Springer Science and Business Media LLC
Date: 10-1985
DOI: 10.1007/BF02746805
Publisher: AIP Publishing
Date: 06-2009
DOI: 10.1063/1.3141534
Abstract: By using the Fourier transforms of the general hydrogenic bound state wave functions (as ultraspherical polynomials), one may find expectation values of arbitrary functions of momentum p. In this manner the effect of a reciprocity perturbation b can be evaluated for all hydrogenic states.
Publisher: IOP Publishing
Date: 15-04-1987
Publisher: World Scientific Pub Co Pte Lt
Date: 20-09-2016
DOI: 10.1142/S0217751X16501530
Abstract: Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the classification group [Formula: see text], which encompasses the standard model gauge group, and thereby determine the full state inventory this includes the definite prediction of quarks with charge [Formula: see text] and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain [Formula: see text] which is not far from the experimental value around the [Formula: see text] mass.
Publisher: AIP Publishing
Date: 08-1993
DOI: 10.1063/1.530049
Abstract: A variety of Lie algebras and certain classes of representations can be constructed using Grassmann variables regarded as Lorentz scalar coordinates belonging to an internal space. The generators are realized as combinations of multilinear products of the coordinates and derivative operators, while the representations emerge as antisymmetric polynomials in the variables and are thus severely restricted. The nature of these realizations and the interconnections between various subalgebras, for N independent complex anticommuting coordinates, is explored. The addition of such Grassmann coordinates to the usual spacetime manifold provides a natural superfield setting for a unified theory of symmetries of elementary particles. The particle content can be further restricted by imposing discrete symmetries (Lie algebra automorphisms). For the case N=5 some anomaly free choices of multiplets are derived through the imposition of specific superfield duality conditions.
Publisher: American Physical Society (APS)
Date: 26-04-1999
Publisher: American Physical Society (APS)
Date: 15-12-1985
Publisher: IOP Publishing
Date: 02-1982
Publisher: American Physical Society (APS)
Date: 11-1990
Publisher: IOP Publishing
Date: 19-04-2006
Publisher: IOP Publishing
Date: 08-11-2006
Publisher: CSIRO Publishing
Date: 1989
DOI: 10.1071/PH890113
Abstract: Quadratic maps of a vector, depending on a vector parameter and any number of scalars, can be reduced to the transformation x ~ ax(l - x) + dy2 and y ~ h(c - x)y, where d = 0, 1 or -1. Such a (3-parameter) set of transformations possesses an extremely rich structure. We have determined the Julia and Mandelbrot sets of this system and have delineated the characteristic types of x-y motion as well as the transition from one regime to the next.
Publisher: IOP Publishing
Date: 19-04-2006
Publisher: Elsevier BV
Date: 04-1971
Publisher: IOP Publishing
Date: 03-1981
Publisher: World Scientific Pub Co Pte Lt
Date: 05-1986
DOI: 10.1142/S0217732386000142
Abstract: Covariant quantization of Fermi-Bose supersymmetric gauge theories is formulated within an enlarged superspace (x µ , θ α , ξ m ) with manifest ξ-supertranslation (=extended BRST) and Sp(2) invariance. In Wess-Zumino gauges, the correct ghost and auxiliary field structure emerges by counting arguments for the (N=1) super-Yang-Mills, conformal and Einstein supergravity cases. The super-Yang-Mills case is analyzed in detail for both supercovariant and Wess-Zumino gauge-fixing, with particular emphasis on the Sp(2) assignments of the ghost superfields.
Publisher: Elsevier BV
Date: 12-1977
Publisher: American Physical Society (APS)
Date: 05-1986
Publisher: IOP Publishing
Date: 07-1976
Publisher: IOP Publishing
Date: 21-05-1997
Publisher: Springer Science and Business Media LLC
Date: 1974
DOI: 10.1007/BF02785448
Publisher: American Physical Society (APS)
Date: 10-1995
Publisher: Springer Science and Business Media LLC
Date: 10-1972
DOI: 10.1007/BF02728550
Publisher: Elsevier BV
Date: 07-1971
Publisher: IOP Publishing
Date: 02-1973
Publisher: American Physical Society (APS)
Date: 15-11-1985
Publisher: American Association of Physics Teachers (AAPT)
Date: 11-1977
DOI: 10.1119/1.10958
Abstract: By explicitly solving the Schrödinger equation for a particle encountering a linear potential hill (V = 0, x & 0 V = V0x/a, 0 & x & a V = V0, x ≳ a), we obtain corrections to the quantum (a → 0) and classical (a → ∞) limits for the transmission coefficient, demonstrating the influence of the range a over which the potential rises.
Publisher: World Scientific Pub Co Pte Lt
Date: 20-12-2015
DOI: 10.1142/S0217751X15502115
Abstract: By attaching three anticommuting Lorentz scalar (color) property coordinates to space–time, with an appropriate extended metric, we unify gravity with chromodynamics: gauge transformations then just correspond to coordinate transformations in the enlarged space–time-property space.
Publisher: AIP Publishing
Date: 09-1998
DOI: 10.1063/1.532513
Abstract: A direct link between a one-loop N-point Feynman diagram and a geometrical representation based on the N-dimensional simplex is established by relating the Feynman parametric representations to the integrals over contents of (N−1)-dimensional simplices in non-Euclidean geometry of constant curvature. In particular, the four-point function in four dimensions is proportional to the volume of a three-dimensional spherical (or hyperbolic) tetrahedron which can be calculated by splitting into birectangular ones. It is also shown that the known formula of reduction of the N-point function in (N−1) dimensions corresponds to splitting the related N-dimensional simplex into N rectangular ones.
Publisher: World Scientific Pub Co Pte Lt
Date: 09-1988
DOI: 10.1142/S0217732388001264
Abstract: It is possible to construct a grand unified model, including gravity, by adjoining further anticommuting coordinates to space-time. We carry out this program for SU(5) and SO(10) unified models curiously, the former is much more economical than the latter and simply requires five complex Grassmann variables ξ m in addition to the four x μ .
Publisher: Elsevier BV
Date: 04-1983
Publisher: IOP Publishing
Date: 04-1976
Publisher: Springer Science and Business Media LLC
Date: 1985
DOI: 10.1007/BF02721519
Publisher: World Scientific Pub Co Pte Lt
Date: 30-01-1995
DOI: 10.1142/S0217732395000284
Abstract: The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson–quark Lagrangian, with the quark (q) and meson (σ, π) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be m q = f π g, m π = 0, m σ = 2m q , and we also find that the quark–meson coupling is [Formula: see text], the three-meson coupling is [Formula: see text] and the four-meson coupling is λ = 2g 2 = g′/f π , where f π ≃ 90 MeV is the pion decay constant and N c = 3 is the color number. By gauging this model one can generate the couplings to the vector mesons ρ and A 1 , including the quark–vector coupling constant g ρ = 2π, g ρππ , gA 1ρπ and the masses m ρ ~ 700 MeV, [Formula: see text] of course the vector and axial currents remain conserved throughout.
Publisher: American Physical Society (APS)
Date: 15-01-1990
Publisher: American Physical Society (APS)
Date: 15-10-1988
Publisher: World Scientific Pub Co Pte Lt
Date: 10-02-2002
DOI: 10.1142/S0217732302006266
Abstract: Once massless quadratically ergent tadpole diagrams are discarded, because they contain no intrinsic scale, it is possible to convert other ergences into logarithmic form, using partial fraction identities this includes the case of quadratic ergences, as has been applied to the linear sigma model. However the procedure must be carried out with due care, paying great attention to correct numerator factors.
Publisher: Elsevier BV
Date: 08-1976
Publisher: American Physical Society (APS)
Date: 07-1997
Publisher: AIP Publishing
Date: 02-1992
DOI: 10.1063/1.529755
Abstract: Results are presented concerning the structure on the real line of the ‘‘universal function’’ which is the fixed point solution of the Feigenbaum–Cvitanovic renormalization group equation associated with period-doubling chaos in quadratic maps. It is shown that the values which the function takes at its turning points can be algebraically characterized by relation to the infinite cycle associated with the original turning point of the map on the interval. These extrema become increasingly numerous as the argument increases, and their locations can be found progressively using knowledge of the previously determined extrema. As well as providing a simple understanding of the structure of the universal function these simple observations may be of assistance in investigating the convergence or asymptotic behavior of approximations to the universal function, and perhaps in providing a ‘‘corrector’’ step to some of these schemes.
Publisher: IOP Publishing
Date: 10-1975
Publisher: IOP Publishing
Date: 10-1975
Publisher: Elsevier BV
Date: 04-2005
Publisher: World Scientific Pub Co Pte Lt
Date: 30-07-1998
DOI: 10.1142/S0217732398001996
Abstract: We show that the finite difference, -iπ 2 m 2 , between quadratic and logarithmic ergent integrals ∫d 4 p[m 2 (p 2 -m 2 ) -2 - (p 2 -m 2 ) -1 ], as encountered in the linear σ-model, is in fact regularization independent.
Publisher: CSIRO Publishing
Date: 1991
DOI: 10.1071/PH910353
Abstract: An algebraic view of supersymmetric quantum mechanics is taken, emphasising the couplings between bosonic and fermionic modes in the supercharges. A class of model Hamiltonians is introduced wherein the fermionic (bosonic) operators are canonical and the bosonic (fermionic) ones satisfy a Lie algebra (superalgebra) whose representation theory permits the complete solution of the model in principle. The kinematical symmetry of such models is also described. The ex les of one and two bosonic models, with 5U(2) and 5U(3) dynamical algebras respectively, are analysed in detail.
Publisher: American Physical Society (APS)
Date: 1995
Publisher: IOP Publishing
Date: 03-1980
Publisher: American Physical Society (APS)
Date: 06-1997
Publisher: World Scientific Pub Co Pte Lt
Date: 10-02-2014
DOI: 10.1142/S0217751X14500237
Abstract: We develop the general relativity of extended spacetime–property for describing events including their properties. The anticommuting nature of property coordinates, augmenting spacetime (x, t), allows for the natural emergence of generations and for the simple incorporation of gauge fields in the spacetime–property sector. With one electric property, this results in a geometrical unification of gravity and electromagnetism, leading to a Maxwell–Einstein Lagrangian plus a cosmological term. Addition of one neutrinic and three chromic properties should lead to unification of gravity with electroweak and strong interactions.
Publisher: IOP Publishing
Date: 06-1983
Publisher: IOP Publishing
Date: 08-1977
Publisher: American Physical Society (APS)
Date: 15-07-1986
Publisher: Springer Science and Business Media LLC
Date: 1974
DOI: 10.1007/BF02801848
Publisher: American Physical Society (APS)
Date: 10-1995
Publisher: IOP Publishing
Date: 05-1979
Publisher: Springer Science and Business Media LLC
Date: 03-1971
DOI: 10.1007/BF02723988
Publisher: Springer Science and Business Media LLC
Date: 11-1978
DOI: 10.1007/BF02770531
Publisher: IOP Publishing
Date: 03-1973
Publisher: Springer Science and Business Media LLC
Date: 11-10-2008
Publisher: American Association of Physics Teachers (AAPT)
Date: 09-1987
DOI: 10.1119/1.14991
Abstract: The stable floating configuration of a long plank of rectangular cross section depends on the relative density of the plank to the fluid and on the ratio of the sides. The complete solution of this metacentric problem is given.
Publisher: World Scientific Pub Co Pte Lt
Date: 30-10-2007
DOI: 10.1142/S0217751X0703827X
Abstract: By ascribing a complex anticommuting variable ζ to each basic property of a field it is possible to describe all the fundamental particles as combinations of only five ζ and understand the occurrence of particle generations. An extension of space-time x to include property then specifies the 'where, when and what' of an event and allows for a generalized relativity where the gauge fields lie in the x - ζ sector and the Higgs fields in the ζ - ζ sector.
Publisher: American Physical Society (APS)
Date: 15-10-1989
Publisher: IOP Publishing
Date: 09-1982
Publisher: World Scientific Pub Co Pte Lt
Date: 03-1988
DOI: 10.1142/S0217751X88000242
Abstract: By associating spin angular momentum with Sp(2) transformations on two Grassmann coordinates, we show how one may formulate spinor wave functions in complete analogy to spherical harmonics for orbital momentum. The relativistic generalization requires a doubling of Grassmann coordinates and a connection may be established with the Dirac equation.
Publisher: IOP Publishing
Date: 04-11-2003
Publisher: AIP Publishing
Date: 02-1973
DOI: 10.1063/1.1666290
Abstract: Given the free propagator of a matrix-valued field φαβ in the form & φαβ(x), φγδ (0)& = (1/2) (δαγδβδ +δαδδβγ − 2cδαβδγδ) Δ (x), we derive an integral representation for the matrix superpropagator & φαβN(x),φγδN(0)& for arbitrary N, and apply this to find the exponentially parametrized gravity superpropagator & |−g(x)|ωgαβ (x), |−g(0)|ωgγδ (0)& with gμν(x) ≡ [exp κφ(x)]μν. Other applications are also mentioned.
Publisher: IOP Publishing
Date: 07-1972
Publisher: IOP Publishing
Date: 11-1976
Publisher: IOP Publishing
Date: 06-1977
Publisher: CSIRO Publishing
Date: 1993
DOI: 10.1071/PH930729
Abstract: Parametric and dispersive representations of self-energy integrals for particles of arbitrary mass in any dimension look very different. We establish their equivalence explicitly and suggest ways in which the parametric form might prove suitable for tackling Schwinger-Dyson equations in gauge theories.
Publisher: IOP Publishing
Date: 07-1981
Publisher: American Physical Society (APS)
Date: 06-1996
Publisher: IOP Publishing
Date: 04-1981
Publisher: Elsevier BV
Date: 11-1975
Publisher: World Scientific Pub Co Pte Lt
Date: 10-11-2013
DOI: 10.1142/S0217751X13300512
Abstract: We describe a geometrical way to unify gravity with the other natural forces by adding fermionic Lorentz scalar variables, characterising attribute or property, to space–time location. (With five such properties one can accommodate all known leptons and quarks.) Using just one property, viz. electricity, the general relativity of such a scheme and its superscalar curvature automatically produces the Einstein–Maxwell Lagrangian and a cosmological term. By adding more properties we envisage the geometrical unification of the standard model with gravitation.
Publisher: World Scientific Pub Co Pte Lt
Date: 30-01-1995
DOI: 10.1142/S0217732395000284
Abstract: The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson–quark Lagrangian, with the quark (q) and meson (σ, π) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be m q = f π g, m π = 0, m σ = 2m q , and we also find that the quark–meson coupling is [Formula: see text], the three-meson coupling is [Formula: see text] and the four-meson coupling is λ = 2g 2 = g′/f π , where f π ≃ 90 MeV is the pion decay constant and N c = 3 is the color number. By gauging this model one can generate the couplings to the vector mesons ρ and A 1 , including the quark–vector coupling constant g ρ = 2π, g ρππ , gA 1ρπ and the masses m ρ ~ 700 MeV, [Formula: see text] of course the vector and axial currents remain conserved throughout.
Publisher: World Scientific Pub Co Pte Lt
Date: 20-02-1990
DOI: 10.1142/S0217732390000421
Abstract: Using five complex, anticommuting internal coordinates θ it is possible to construct suitable Lagrangians for matter fields in three generations. We demonstrate how to do this using appropriate superfields for source and Higgs fields.
Publisher: IOP Publishing
Date: 05-1975
Publisher: IOP Publishing
Date: 21-02-1987
Publisher: World Scientific Pub Co Pte Lt
Date: 27-05-2016
DOI: 10.1142/S0217732316300159
Abstract: Local events are characterized by “where”, “when” and “what”. Just as (bosonic) spacetime forms the backdrop for location and time, (fermionic) property space can serve as the backdrop for the attributes of a system. With such a scenario I shall describe a scheme that is capable of unifying gravitation and the other forces of nature. The generalized metric contains the curvature of spacetime and property separately, with the gauge fields linking the bosonic and fermionic arenas. The super-Ricci scalar can then automatically yield the spacetime Lagrangian of gravitation and the Standard Model (plus a cosmological constant) upon integration over property coordinates.
Publisher: AIP Publishing
Date: 04-1972
DOI: 10.1063/1.1666001
Abstract: We apply (Laplace, Fourier, …) transform methods to obtain compact representations of the perturbation S-matrix elements for interaction Lagrangians which are general nonpolynomial functions of isospin multiplets. In order to illustrate the power and simplicity of the method for coping with the isospin complications, we have treated several ex les in detail, and these include the commonly used parametrizations of the unitary chiral SU(2)⊗SU(2) transformations.
Publisher: CSIRO Publishing
Date: 1991
DOI: 10.1071/PH910135
Abstract: We show that a limited range of options for fermion families may be neatly encompassed in a spacetime augmented by five Grassmann internal coordinates if we require that the superfields are self-dual in an 5U(5) sense. Amongst the possibilities is a family of just three standard model generations. We consider the nature of Higgs fields in this formalism and the form of possible gauge symmetries.
Publisher: AIP Publishing
Date: 06-1985
DOI: 10.1063/1.526941
Abstract: Gravitational contributions to the chiral anomaly in 4N space-time dimensions as well as the purely gravitational anomaly in 4N−2 dimensions are expressed in terms of the Riemann–Christoffel tensor. Using this formula, we give a simple proof that if N≥4 there is no way to cancel the gravitational anomalies using fields of spin- 1/2 , - 3/2 , and -1.
Publisher: IOP Publishing
Date: 12-1982
Publisher: IOP Publishing
Date: 07-1980
Publisher: American Physical Society (APS)
Date: 1996
Publisher: CSIRO Publishing
Date: 1997
DOI: 10.1071/PP96075
Abstract: Although some theoretical predictions have been made, no experimental evidence of chaotic behaviour in plant physiological responses has been reported. Here we present observations of period- doubling and tripling in higher plants. For leaf bioelectric and temperature responses of maize, tomato, and burweed plants to rhythmical light, two different routes to chaos were found experimentally. One was via successive period-doubling and the other via the formation of intermittently chaotic oscillations from a subharmonic synchronisation. Because these effects appeared in intact plants, under conditions close to those found in nature, they may have wide significance, including for plant phylogenesis.
Publisher: IOP Publishing
Date: 28-02-2000
Publisher: World Scientific Pub Co Pte Lt
Date: 20-08-1992
DOI: 10.1142/S0217751X92002386
Abstract: The gauge interaction and mass generation through the Higgs mechanism is worked out for a Grassmannian SU(5) model, which among many other states, predicts three light neutrinos and two heavy ones. It is found that Simpson’s 17 keV neutrino remains incompatible with the MSW solution to the solar neutrino puzzle in this framework
Publisher: World Scientific Pub Co Pte Lt
Date: 02-1988
DOI: 10.1142/S0217732388000362
Abstract: Within the formalism of OSp(D/2) supersymmetry, wherein extended BRST transformations correspond to supertranslations, we fix the gauge of bosonic stringlike models in the form, ∂g=0, [Formula: see text]. The action has no propagating or interacting conformal ghosts and the Sp(2) symmetry between the ghosts is manifest.
Publisher: Springer Science and Business Media LLC
Date: 09-1974
DOI: 10.1007/BF02739481
Publisher: AIP Publishing
Date: 04-1991
DOI: 10.1063/1.529382
Abstract: The two-frequency quasiperiodic route to chaos is believed to be modeled by the critical circle map and the universal behavior of the scaling constants α and δ is determined by the order z of the inflection point. We have numerically determined α(z) and δ(z) as a function of this order. Using the renormalization group equations, we have succeeded in obtaining approximate analytical relations for α and δ that agree quite well with the data. In the limit as z→∞, we argue that ‖δ‖→1/ρ3=4.236 and δ/αz→1, in good agreement with the numerical computations.
Publisher: Springer Science and Business Media LLC
Date: 09-1974
DOI: 10.1007/BF02739482
Publisher: Elsevier BV
Date: 10-1972
Publisher: IOP Publishing
Date: 05-1984
Publisher: American Physical Society (APS)
Date: 24-11-1986
Publisher: AIP Publishing
Date: 12-2001
DOI: 10.1063/1.1416887
Abstract: We derive expressions for the phase space of a particle of momentum p decaying into N particles, that are valid for any number of dimensions. These are the imaginary parts of so-called “sunset” diagrams, which we also obtain. The results are given as a series of hypergeometric functions, which terminate for odd dimensions and are also well suited for deriving the threshold behavior.
Publisher: Elsevier BV
Date: 1996
Publisher: IOP Publishing
Date: 21-12-1984
Publisher: CSIRO Publishing
Date: 1992
DOI: 10.1071/PH920621
Abstract: Assuming that space-time is accompanied by hidden anticommuting coordinates, we have constructed 'fermionic' eneralisations of the Dirac equation these equations involve matrices (which can be construed as operating in an internal space) multiplying the Grassmann derivatives. We discuss several models, of varying degrees of complexity, with 'internal symmetries' including Sp(2) and S (N). By appending the space-time Dirac operator, one is led to mass spectra with quantised alues, suggesting that this approach may provide a model relating generations to internal symmetries.
Publisher: Springer Science and Business Media LLC
Date: 04-1980
DOI: 10.1007/BF02750301
Publisher: Springer Science and Business Media LLC
Date: 03-1975
DOI: 10.1007/BF02790603
Publisher: Elsevier BV
Date: 02-1984
Publisher: American Physical Society (APS)
Date: 05-1998
Publisher: IOP Publishing
Date: 02-1979
Publisher: Springer Science and Business Media LLC
Date: 03-1975
DOI: 10.1007/BF02790604
Publisher: CSIRO Publishing
Date: 1999
DOI: 10.1071/PH99018
Abstract: A summary of the successes of and obstacles to the gauge technique (a non-perturbative method of solving Dyson–Schwinger equations in gauge theories) is given, as well as an outline of how progress may be achieved in this field.
Publisher: World Scientific Pub Co Pte Lt
Date: 04-1987
DOI: 10.1142/S0217732387000380
Abstract: The effect of Pauli interactions on the scaling anomaly is to add F 4 , (∂F) 2 and m 2 F 2 terms to the trace of the stress-tensor at one loop level, such terms being connected with renormalisation. However, when the sum over all modes is taken, these extra contributions vanish upon zeta-function regularisation.
Publisher: World Scientific Pub Co Pte Lt
Date: 20-09-1992
DOI: 10.1142/S0217751X92002659
Abstract: The principal attraction of the Fock-Schwinger (FS) gauge is that the gauge potentials are completely determined in terms of the electromagnetic fields by an inversion formula once the condition x·A=0 is fixed. We have reformulated the FS gauge propagator, first derived by Kummer and Weiser, in a more useful and manageable form and applied it to perturbation calculations in spinor and scalar QED and QCD. In that way we have been able to verify the on-mass-shell equivalence of these calculations to the covariant Feynman gauge.
Publisher: AIP Publishing
Date: 1987
DOI: 10.1063/1.527808
Abstract: For complex mappings of the type z→λz(1−z), universality constants α and δ can be defined along islands of stability lying on filamentary sequences in the complex λ plane. As the end of the filament is approached, asymptotic values αN∼λN−1∞, δN/α2N∼1 are attained, where μ∞=λ∞(λ∞−2)/4, is associated with the limiting form of the universal function for that sequence, g(z)=1−μ∞z2. These results are complex generalizations of the real mapping case (applying to tangent bifurcations and windows of stability) where μ∞=2 and δ/α2→ (2)/(3) correspond to the filament running along the real axis.
Publisher: Springer Science and Business Media LLC
Date: 02-1979
DOI: 10.1007/BF02815780
Publisher: AIP Publishing
Date: 08-1999
DOI: 10.1063/1.532950
Abstract: We define a special matrix multiplication among a special subset of 2N×2N matrices, and study the resulting (nonassociative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative nonassociative, and when they become associative. In particular, these algebras yield special matrix representations of octonions and complex numbers they naturally lead to the Cayley–Dickson doubling process. Our matrix representation of octonions also yields elegant insights into Dirac’s equation for a free particle. A few other results and remarks arise as byproducts.
Publisher: IOP Publishing
Date: 05-2006
Publisher: World Scientific Pub Co Pte Lt
Date: 20-08-1994
DOI: 10.1142/S0217732394002173
Abstract: A new principle of ‘schizosymmetry’ is proposed for interpreting superfield expansions over Grassmann parameters in quantum field theory. Symmetry generators T phys , determining component field transformation properties, are allowed to depend on the grading via T phys =Tℙ e +T′ℙ o , where ℙ e and ℙ o are the projections onto even and odd components in the Grassmann coordinates, respectively, and T and T′ correspond to different representations. Ex les are given for both internal and space-time schizosymmetry. In the latter case, superfield expansions have components with both integer and half-integer spin. A program for the Lagrangian realization of schizosymmetry, including unified model building, is outlined.
Publisher: IOP Publishing
Date: 12-1977
Publisher: IOP Publishing
Date: 05-1975
Publisher: Elsevier BV
Date: 03-1988
Publisher: IOP Publishing
Date: 1977
Publisher: CSIRO Publishing
Date: 1994
DOI: 10.1071/PH940465
Abstract: One of the interesting features about field theories in odd dimensions is the induction of parity-violating terms and well-defined finite topological actions via quantum loops if a fermion mass term is originally present and conversely. Aspects of this issue are illustrated for electrodynamics in 2+ 1 and 4+ 1 dimensions.
Publisher: Springer Science and Business Media LLC
Date: 06-1972
DOI: 10.1007/BF02785254
Publisher: American Physical Society (APS)
Date: 11-1983
Publisher: AIP Publishing
Date: 05-1973
DOI: 10.1063/1.1666358
Abstract: The techniques developed in a previous paper (I) to compute the T product 〈φNαβ(x), φNγδ(o)〉 for arbitrary N are extended to cover the case when φ(x) is a Hermitian matrix-valued field in ν dimensions. We obtain a closed expression which is used to determine superpropagators like 〈[expκφ(x)]αβ, [expκφ(o)]γδ〉, which occur in strong interaction physics when φ is an SU(3) field, say.
Publisher: World Scientific Pub Co Pte Lt
Date: 18-01-2012
DOI: 10.1142/S021773231650019X
Abstract: We determine the coefficients of the terms multiplying the gauge fields, gravitational field and cosmological term in a scheme whereby properties are characterized by N anticommuting scalar Grassmann variables. We do this for general N, using analytical methods this obviates the need for our algebraic computing package which can become quite unwieldy as N is increased.
Publisher: World Scientific Pub Co Pte Lt
Date: 10-11-1999
DOI: 10.1142/S0217751X99002086
Abstract: We exhibit the one-loop multigluon effective Lagrangian in any dimension for a field theory with a quasilocal background, using the background-field formalism. Specific results, including counterterms (up to 12 space–time dimensions), have been derived, applied to the Yang–Mills theory and found to be in agreement with other string-inspired approaches.
Publisher: IOP Publishing
Date: 12-1979
Publisher: World Scientific Pub Co Pte Lt
Date: 10-02-1998
DOI: 10.1142/S0217751X98000299
Abstract: This paper is the SU(3) extension of the dynamically generated SU(2) linear σ model Lagrangian worked out previously using dimensional regularization. After discussing the quark-level Goldberger–Treiman relations for SU(3) and the related gap equations, we dynamically generate the meson cubic and quartic couplings. This also constrains the meson–quark coupling constant to [Formula: see text] and determines the SU(3) scalar meson masses in a Nambu–Jona-Lasinio fashion. Finally we dynamically induce the U(3) pseudoscalar and scalar mixing angles in a manner compatible with data.
Publisher: IOP Publishing
Date: 08-1978
Publisher: Springer Science and Business Media LLC
Date: 11-1970
DOI: 10.1007/BF02755264
Publisher: IOP Publishing
Date: 11-1977
Publisher: World Scientific Pub Co Pte Lt
Date: 30-10-1999
DOI: 10.1142/S0217751X99002049
Abstract: We show that all abnormal parity three-body meson interactions can be adequately described by quark loops, evaluated at zero external momentum, with couplings determined by U(N f ) symmetry. We focus primarily on radiative meson decays which involve one pseudoscalar. The agreement with experiment for nonrare decays is surprisingly good and requires very few parameters, namely the coupling constants g πqq and g ρqq and some mixing angles. This agreement extends to some three-body decays that are dominated by pion pairs in a P-wave state.
Publisher: Elsevier BV
Date: 06-1983
Publisher: CSIRO Publishing
Date: 2013
DOI: 10.1071/HR12020
Abstract: Graeme Reade Anthony Ellis (universally known as ?Bill') was a pioneer in the area of low-frequency radio observations. By exploiting Hobart's geomagnetic latitude and the lack of background radio noise there, he was able to make major discoveries at these low frequencies (principally in the frequency range 1?10�MHz).Among the questions he pursuedwere the propagation/dispersion/reflection of radio waves in the ionosphere and the detection of radio emissions from the Sun, the galactic disk and Jupiter. He built innovative radio receivers and de-dispersers to gain information about the radio sources, for ex le about the Sun via aurorae and about the influence of Io on the Jovian emissions. It is thanks to Ellis' practical research investigations and clever experimental methods that radio astronomy at the University of Tasmania is today firmly established and internationally recognized.
Publisher: Oxford University Press (OUP)
Date: 1994
Publisher: IOP Publishing
Date: 05-05-2000
Publisher: IOP Publishing
Date: 02-1980
Publisher: World Scientific Pub Co Pte Lt
Date: 09-01-2015
DOI: 10.1142/S0217751X15500050
Abstract: We demonstrate that the extension of the space–time metric to incorporate two anticommuting property coordinates automatically leads to the unification of gravity with non-Abelian gauge theory, as well as producing a cosmological term.
Publisher: Springer Science and Business Media LLC
Date: 09-1972
DOI: 10.1007/BF02905266
Publisher: IOP Publishing
Date: 29-01-2003
Publisher: IOP Publishing
Date: 10-06-2004
Publisher: IOP Publishing
Date: 03-1976
Publisher: American Physical Society (APS)
Date: 15-10-1996
Publisher: American Physical Society (APS)
Date: 25-10-1999
Publisher: World Scientific Pub Co Pte Lt
Date: 02-1988
DOI: 10.1142/S0217751X88000163
Abstract: Various massive Yang-Mills theories not based on the Higgs mechanism are investigated. They are subject to conflicting demands in the twin requirements of unitarity and perturbative renormalizability. Either one or other of these requirements is violated. Unitarity is considered in some detail.
Publisher: AIP Publishing
Date: 06-2009
DOI: 10.1063/1.3141534
Abstract: By using the Fourier transforms of the general hydrogenic bound state wave functions (as ultraspherical polynomials), one may find expectation values of arbitrary functions of momentum p. In this manner the effect of a reciprocity perturbation b can be evaluated for all hydrogenic states.
Publisher: IOP Publishing
Date: 07-1981
Publisher: World Scientific Pub Co Pte Lt
Date: 30-10-1992
DOI: 10.1142/S0217751X9200315X
Abstract: Infrared singularities in QED 3 can be avoided by including at least one massless source which couples to the photon. Once that is arranged it is possible to obtain nonzeromass solutions for the source Green functions in scalar and (doubled) spinor electrodynamics, by using the gauge technique. We find that the asymptotic results for the source spectral ρ functions are typically ρ(p)≃(p 2 −m 2 ) −1−e 2 /cπ 2 as p→m, and ρ(p)≃p −2 exp (c′e 2 /πp) as p→∞. The constants c and c′ are respectively related to the number of charged massless particles and their “spin” character.
Publisher: IOP Publishing
Date: 10-1978
Publisher: Elsevier BV
Date: 08-1976
Publisher: Springer Science and Business Media LLC
Date: 05-1974
DOI: 10.1007/BF02731185
Publisher: American Physical Society (APS)
Date: 15-04-1997
Publisher: IOP Publishing
Date: 15-04-2004
Publisher: IOP Publishing
Date: 09-1982
Publisher: Elsevier BV
Date: 02-1982
Publisher: World Scientific Pub Co Pte Lt
Date: 20-06-2015
DOI: 10.1142/S0217751X15500955
Abstract: The standard model ascribes distinct properties to different chiralities of fermions. We show how to incorporate this aspect in an extended space–time-property framework involving two different attributes using a generalized metric which includes gauge fields as well as gravitation. Because the gauge fields are accompanied by coupling constants, all such schemes, including ours, necessitate coupling unification at high energy to ensure universality of gravitational interactions with matter.
Publisher: Springer Science and Business Media LLC
Date: 02-1975
DOI: 10.1007/BF02729305
Publisher: IOP Publishing
Date: 04-1982
Publisher: World Scientific Pub Co Pte Lt
Date: 20-01-1996
DOI: 10.1142/S0217751X96000122
Abstract: The subject of low energy photon-photon scattering is considered in arbitrary-dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalization resolves the structure of the weak field Euler-Heisenberg Lagrangian and indicates that the component invariant functions have coefficients related not only to the space-time dimension but also to the coefficients of the Bernoulli polynomial.
Publisher: IOP Publishing
Date: 21-05-1997
Publisher: IOP Publishing
Date: 04-1981
Publisher: Elsevier BV
Date: 1999
Publisher: CSIRO Publishing
Date: 1986
DOI: 10.1071/PH860189
Abstract: Empirical and analytical evidence is presented for the relation 8 N = {( z - 1) / (z - D) a N between the universal constants describing the approach to the accumulation points, for cycles undergoing multiplication by period N, in one-dimensional maps possessing an order z maximum
Publisher: IOP Publishing
Date: 05-05-2000
Publisher: World Scientific Pub Co Pte Lt
Date: 10-1986
DOI: 10.1142/S0217732386000579
Abstract: A general procedure for defining gauge-invariant fields is presented. In this way it is possible to associate gauge-variant Green functions, in some particular gauge, with gauge-invariant quantities. This construction can be done regardless of whether a mass shell exists or not and should be useful for the colored sector in quantum chromodynamics.
Publisher: Wiley
Date: 10-10-2013
Publisher: World Scientific Pub Co Pte Lt
Date: 20-07-1989
DOI: 10.1142/S021773238900157X
Abstract: We show that five complex anticommuting coordinates are sufficient to describe the present particle spectrum, including the possibility of understanding the generation problem.
Publisher: Elsevier BV
Date: 09-1974
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Robert Delbourgo.