Stress Tensor Correlators in the Schwinger-Keldysh Formalism

TL;DR

This paper reformulates stress tensor correlators within the Schwinger-Keldysh formalism, demonstrating divergence properties and regularization techniques at one-loop order for a massless scalar field in flat spacetime.

Contribution

It provides a novel application of the Schwinger-Keldysh formalism to stress tensor correlators, clarifying divergence structures and regularization methods.

Findings

+- and -+ correlators are divergence-free due to absence of off-diagonal counterterms

The ++ correlator contains known divergences in scalar graviton self-energy

Dimensional regularization effectively checks divergence properties at one loop

Abstract

We express stress tensor correlators using the Schwinger-Keldysh formalism. The absence of off-diagonal counterterms in this formalism ensures that the +- and -+ correlators are free of primitive divergences. We use dimensional regularization in position space to explicitly check this at one loop order for a massless scalar on a flat space background. We use the same procedure to show that the ++ correlator contains the divergences first computed by `t Hooft and Veltman for the scalar contribution to the graviton self-energy.