Energy-momentum tensors with worldline numerics

TL;DR

This paper introduces a numerical worldline Monte-Carlo method to compute energy-momentum tensors for fluctuating scalar fields, enabling efficient analysis of quantum field energy conditions.

Contribution

It derives explicit worldline expressions for the energy-momentum tensor components and demonstrates their numerical evaluation for the first time.

Findings

Efficient numerical evaluation of energy-momentum tensors is feasible.

Explicit worldline formulas simplify calculations.

Method can investigate positive-energy conditions.

Abstract

We apply the worldline formalism and its numerical Monte-Carlo approach to computations of fluctuation induced energy-momentum tensors. For the case of a fluctuating Dirichlet scalar, we derive explicit worldline expressions for the components of the canonical energy-momentum tensor that are straightforwardly accessible to partly analytical and generally numerical evaluation. We present several simple proof-of-principle examples, demonstrating that efficient numerical evaluation is possible at low cost. Our methods can be applied to an investigation of positive-energy conditions.