Quantum inequalities for the free Rarita-Schwinger fields in flat spacetime

TL;DR

This paper derives a quantum inequality for free massive spin-3/2 Rarita-Schwinger fields in flat spacetime, revealing it is weaker than for spin-1/2 Dirac fields, and suggests a relation between degrees of freedom and inequality strength.

Contribution

It provides the first quantum inequality bound for Rarita-Schwinger fields and proposes a conjecture linking the number of degrees of freedom to the strength of quantum inequalities.

Findings

Quantum inequality for Rarita-Schwinger fields derived.

The bound is weaker by a factor of 2 compared to Dirac fields.

Conjecture that more degrees of freedom lead to weaker quantum inequalities.

Abstract

Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin-${3\over 2}$ Rarita-Schwinger fields in the four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin-${1\over 2}$ Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in the flat spacetime, separately for bosonic and fermionic fields, the quantum inequality bound gets weaker as the the number of degrees of freedom of the field increases. A plausible physical reason might be that the more the number of field degrees of freedom, the more freedom one has to create negative energy, therefore, the weaker the quantum inequality bound.