[Show abstract][Hide abstract] ABSTRACT: A detailed study of certain apspects of some 2+1 dimensional field theories is presented with special emphasis on the role of Wigner's little group for massless particles in generating gauge transformations. The planar models considered here include topologically massive gauge theories like Maxwell-Chern-Simons(MCS) and Einstein-Chern-Simons (ECS) theories, non-gauge theories such as Maxwell-Chern-Simons-Proca(MCSP) and Einstein-Pauli-Fierz(EPF) models and also the Stuckelberg embedded gauge invariant versions of many massive theories. Using polarization vectors/tensors, several interrelationships between various theories are uncovered and related issues are elucidated. It is shown that the translational subgroup of Wigner's little group for massless particles generate the momentum-space gauge transformations in all the Abelian gauge theories considered here. While the defining representation of the little group generates gauge transformations in massless gauge theories, a different representation is shown to be necessary in the case of gauge theories having massive excitations. The analysis of the gauge generating nature of the translational group is also extended to theories living in higher space-time dimensions. A method named (\it dimensional descent} is used to systematically derive the polarization vector/tensor and the gauge transformation property of a lower dimensional theory from those of an appropriate higher dimensional theory.
[Show abstract][Hide abstract] ABSTRACT: We examine the gauge generating nature of the translational subgroup of Wigner's little group for the case of massless tensor gauge theories and show that the gauge transformations generated by the translational group is only a subset of the complete set of gauge transformations. We also show that, just like the case of topologically massive gauge theories, translational groups act as generators of gauge transformations in gauge theories obtained by extending massive gauge noninvariant theories by a Stuckelberg mechanism. The representations of the translational groups that generate gauge transformations in such Stuckelberg extended theories can be obtained by the method of dimensional descent. We illustrate these with the examples of Stuckelberg extended first class versions of Proca, Einstein-Pauli-Fierz and massive Kalb-Ramond theories in 3+1 dimensions. A detailed analysis of the partial gauge generation in massive and massless 2nd rank symmetric gauge theories is provided. The gauge transformations generated by translational group in 2-form gauge theories are shown to explicitly manifest the reducibility of gauge transformations in these theories. Comment: Latex, 20 pages, no figures, Version to appear in Physical Review D
[Show abstract][Hide abstract] ABSTRACT: We show that the translational subgroup of Wigner's little group for massless particles in 3+1 dimensions generate gauge transformation in linearized Einstein gravity. Similarly a suitable representation of the 1-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2+1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3+1 and 2+1 dimensions. Finally, the polarization tensor of Einstein-Pauli-Fierz theory in 2+1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for Einstein-Pauli-Fierz theory. Comment: Latex, 22 pages, no figures, To appear in Class. Quant. Grav
Preview · Article · May 2002 · Classical and Quantum Gravity
[Show abstract][Hide abstract] ABSTRACT: The noncommutative star product of phase space functions is, by construction, associative for both non-degenerate and degenerate case (involving only second class constraints) as has been shown by Berezin, Batalin and Tyutin. However, for the latter case, the manifest associativity is lost if an arbitrary coordinate system is used but can be restored by using an unconstrained canonical set. The existence of such a canonical transformation is guaranteed by a theorem due to Maskawa and Nakajima. In terms of these new variables, the Kontsevich series for the star product reduces to an exponential series which is manifestly associative. We also show, using the star product formalism, that the angular momentum of a particle moving on a circle is quantized.
[Show abstract][Hide abstract] ABSTRACT: We establish the equivalence of the Maxwell-Chern-Simons-Proca model to a doublet of Maxwell-Chern-Simons models at the level of polarization vectors of the basic fields using both Lagrangian and Hamiltonian formalisms. The analysis reveals a U(1) invariance of the polarization vectors in the momentum space. Its implications are discussed. We also study the role of Wigner's little group as a generator of gauge transformations in three space-time dimensions. Comment: LaTex, 30 pages, no figures
Full-text · Article · Nov 2000 · International Journal of Modern Physics A