Chiral spin-$3/2$ particles in a medium

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 explicitly 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.

Figure 1

Vertex diagram for the spin-$3/2$ particle ${\lambda }_{L\mu }$ with the spin-$1/2$ fermion $f$ and the scalar particle $A$. The vertex function $V_{\mu }(k)$ is given in Eq. (6.2).

Figure 2

Diagram for the self-energy of the spin-$3/2$ particle ${\lambda }_L$ in the background of the spin-$1/2$ fermion $f$ and the scalar particle $A$.