How unique is the expected stress-energy tensor of a massive scalar field?

TL;DR

This paper investigates the ambiguities in the expected stress-energy tensor of a massive scalar field, revealing a much larger set of free parameters compared to the massless case, and provides a method to compute it on perturbed Minkowski spacetime.

Contribution

It demonstrates that the ambiguity in the renormalized stress-energy tensor for a massive scalar field is significantly larger than for a massless one and extends previous calculations to massive fields.

Findings

Ambiguities in the stress-energy tensor are infinite for massive fields.

The formalism applies to any linear perturbation of Minkowski spacetime.

Provides a generalized calculation method for massive scalar fields.

Abstract

We show that the set of ambiguities in the renormalized expected stress-energy tensor allowed by the Wald axioms is much larger for a massive scalar field (an infinite number of free parameters) than for a massless scalar field (two free parameters). We also use the closed-time-path effective action formalism of Schwinger to calculate the expected value of the stress-energy tensor in the incoming vacuum state, for a massive scalar field, on any spacetime which is a linear perturbation off Minkowski spacetime. This result generalizes an earlier result of Horowitz and also Jordan in the massless case, and can be used as a testbed for comparing different calculational methods.