Chiral spin-3/2 particles in a medium

TL;DR

This paper develops a theoretical framework using Thermal Field Theory to analyze the propagation and dispersion relations of chiral spin-3/2 particles in a medium, providing explicit calculations in a specific model.

Contribution

It introduces a systematic method to derive dispersion relations for chiral spin-3/2 particles in a medium, extending techniques used for lower-spin particles.

Findings

Multiple propagation modes identified with explicit dispersion relations.

Explicit 1-loop TFT calculations for a specific model.

Analogies and differences with photon and fermion cases analyzed.

Abstract

We consider the propagation of a chiral spin-3/2 particle in a background medium using the Thermal Field Theory (TFT) method, in analogy to the cases of a spin-1/2 fermion (e.g., a neutrino) and the photon. We present a systematic decomposition of the thermal self-energy, from which the dispersion relation of the modes that propagate in the medium are obtained. We find that there are several modes and in each case we obtain the equation for the dispersion relation as well as the corresponding spin-3/2 spinor. As an example of the general procedure and results, we consider a model in which the chiral spin-3/2 particle couples to a spin-1/2 fermion and a scalar particle, and propagates in a thermal background composed of such particles. The dispersion relations and corresponding spinors are detemined explcitly in this case from the 1-loop TFT expression for the self-energy. The results in this case share some resemblance and analogies with the photon and the chiral fermion cases but, as already noted, there are also differences. The present work provides the groundwork for considering problems related to the properties of chiral spin-3/2 particles in a medium, in analogy to the case of neutrinos for example, which can be relevant in physical contexts of current interest.