SPIN ROTATION UNDER LORENTZ TRANSFORMATIONS AND ITS GEOMETRIC INTERPRETATIONS

Authors

  • B. A. Rajabov

Keywords:

Poincarè group ISO(3, 1), spherical geometry, hyperbolic geometry, , unitary ray representations, small group, Wigner's operator

Abstract

This review presents the main points of the theory of Wigner's representations of the quantum-mechanical Poincarè group ISO(3, 1) and its application in the theory of elementary particles. Explicit formulas for the angles of rotation of the spin during Lorentz turns, as well as geometric interpretations of the results of Wigner's theory in terms of spherical and hyperbolic geometries are given. The results admit a direct generalization to cosmological groups SO(4, 1) and SO(3, 2).

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Published

2024-03-07

Issue

Vol. 14 No. 1 (2019)

Section

Articles