Vacuum stress-tensor in SSB theories

TL;DR

This paper investigates the covariant implementation of momentum cut-offs and the conservation of the vacuum energy-momentum tensor in theories with Spontaneous Symmetry Breaking, confirming the general conservation law holds in these complex cases.

Contribution

It demonstrates that the conservation laws for the vacuum energy-momentum tensor remain valid in Spontaneous Symmetry Breaking theories with a covariant momentum cut-off.

Findings

Covariant momentum cut-off can be implemented consistently.

Conservation laws hold in SSB theories despite complex calculations.

Final results confirm covariance and conservation in SSB contexts.

Abstract

The renormalized energy-momentum tensor of vacuum has been deeply explored many years ago. The main result of these studies was that such a tensor should satisfy the conservation laws which reflects the covariance of the theory in the presence of loop corrections. In view of this general result we address two important questions, namely how to implement the momentum cut-off in a covariant way and whether this general result holds in the theory with Spontaneous Symmetry Breaking. In the last case some new interesting details arise and although the calculations are more involved we show that the final result satisfies the conservation laws.