Stokes Parameters as a Minkowskian Four-vector

It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This four-by-four formalism can deal with partial coherence described by the Stokes parameters. A four-by-four matrix formulation is given for decoherence effects on the Stokes parameters, and a possible experiment is proposed. It is shown also that this Lorentz-group formalism leads to optical filters with a symmetry property corresponding to that of two-dimensional Euclidean transformations.Comment: RevTeX, 22 pages, no figures, submitted to Phys. Rev.

Iwasawa Effects in Multi-layer Optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and one time-like dimensions, or the $Sp(2)$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S-matrix for transmitted and reflected rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.Comment: RevTex 10 pages including 1 psfi

Feynman's Decoherence

Gell-Mann's quarks are coherent particles confined within a hadron at rest, but Feynman's partons are incoherent particles which constitute a hadron moving with a velocity close to that of light. It is widely believed that the quark model and the parton model are two different manifestations of the same covariant entity. If this is the case, the question arises whether the Lorentz boost destroys coherence. It is pointed out that this is not the case, and it is possible to resolve this puzzle without inventing new physics. It is shown that this decoherence is due to the measurement processes which are less than complete.Comment: RevTex 15 pages including 6 figs, presented at the 9th Int'l Conference on Quantum Optics (Raubichi, Belarus, May 2002), to be published in the proceeding

Translational groups as generators of gauge transformations

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

Wigner's little group and BRST cohomology for one-form Abelian gauge theory

We discuss the (dual-)gauge transformations for the gauge-fixed Lagrangian density and establish their intimate connection with the translation subgroup T(2) of the Wigner's little group for the free one-form Abelian gauge theory in four $(3 + 1)$-dimensions (4D) of spacetime. Though the relationship between the usual gauge transformation for the Abelian massless gauge field and T(2) subgroup of the little group is quite well-known, such a connection between the dual-gauge transformation and the little group is a new observation. The above connections are further elaborated and demonstrated in the framework of Becchi-Rouet-Stora-Tyutin (BRST) cohomology defined in the quantum Hilbert space of states where the Hodge decomposition theorem (HDT) plays a very decisive role.Comment: LaTeX file, 17 pages, Journal-ref. give

Pulsars in FIRST Observations

We identified 16 pulsars from the Faint Images of the Radio Sky at Twenty-cm (FIRST) at 1.4 GHz. Their positions and total flux densities are extracted from the FIRST catalog. Comparing the source positions with those in the PSRcatalog, we obtained better determined positions of PSRs J1022+1001, J1518+4904, J1652+2651, and proper motion upper limits of another three pulsars PSRs J0751+1807, J1012+5307, J1640+2224. Proper motions of the other 10 pulsars are consistent with the values in the catalog.Comment: 6 pages, 2 figures, 3 tables, submited to CJA