Affiliation: Arizona State University
Title Of Talk: Symmetry in Physics: a Way from Poincare Group Representations to Relativistic Wave Equations
Abstract: We analyze kinematics of the fundamental relativistic wave equations, in a traditional way, from the viewpoint of the representation theory of the Poincaré group. In particular, the importance of the Pauli-Lubański pseudo-vector is emphasized here not only for the covariant definition of spin and helicity of a given field but also for the derivation of the corresponding equation of motion. In this consistent group-theoretical approach, the resulting wave equations occur, in general, in certain overdetermined forms, which can be reduced to the standard ones by a matrix version of Gaussian elimination. Although, mathematically, all representations of the Poincaré group are locally equivalent, their explicit realizations in conventional linear spaces of four-vectors and tensors, spinors and bispinors, etc. are quite different from the viewpoint of physics. This is why, the corresponding relativistic wave equations are so different. Among them we concentrate on Dirac's equations, Weyl's two-component equation for massless neutrinos, and the Proca, Maxwell, and Fierz-Pauli equations. The case of linearized Einstein's equations for weak gravitational fields is also discussed.
Last update made Sat Feb 20 08:48:07 PST 2016.