Kinematical formalism of elementary spinning particles

TL;DR

This paper develops a kinematical framework for elementary spinning particles, linking their spin structure to homogeneous spaces of symmetry groups, and quantizes the model using Feynman's path integral, connecting classical and quantum descriptions.

Contribution

It introduces a formalism relating spin to homogeneous spaces of symmetry groups and explores its quantization, including classical models satisfying Dirac's equation.

Findings

Spin structure linked to homogeneous spaces of symmetry groups

Quantization via Feynman's path integral approach

Classical models satisfying Dirac's equation analyzed

Abstract

The concept of elementary particle rests on the idea that it is a physical system with no excited states, so that all possible kinematical states of the particle are just kinematical modifications of any one of them. The way of describing the particle attributes is equivalent to describe the collection of consecutive inertial observers who describe the particle in the same kinematical state. The kinematical state space of an elementary particle is a homogeneous space of the kinematical group. By considering the largest homogeneous spaces of both, Galilei and Poincar\'e groups, it is shown how the spin structure is related to the different degrees of freedom. The formalism is quantized by means of Feynman's path integral approach and special attention is paid to the classical model which satisfies Dirac's equation. Dirac's algebra is related to the classical observables, in particular to the orientation variables. Several spin effects are also analyzed.