Energy Momentum Tensor and Operator Product Expansion in Local Causal Perturbation Theory

TL;DR

This paper develops algebraic relations for interacting fields in local perturbative quantum field theory, providing explicit covariant formulas, analyzing energy-momentum tensors, and establishing an operator product expansion framework.

Contribution

It introduces explicit covariant formulas for time ordered products, analyzes energy-momentum tensor conservation and anomalies, and defines an interacting bilocal normal product for scalar theories.

Findings

Conservation of energy-momentum tensor in large class of theories

Existence of an improved traceless tensor in classical theories

Operator product expansion for time ordered fields

Abstract

We derive new examples for algebraic relations of interacting fields in local perturbative quantum field theory. The fundamental building blocks in this approach are time ordered products of free (composed) fields. We give explicit formulas for the construction of Poincare covariant ones, which were already known to exist through cohomological arguments. For a large class of theories the canonical energy momentum tensor is shown to be conserved. Classical theories without dimensionful couplings admit an improved tensor that is additionally traceless. On the example of phi^4-theory we discuss the improved tensor in the quantum theory. Its trace receives an anomalous contribution due to its conservation. Moreover we define an interacting bilocal normal product for scalar theories. This leads to an operator product expansion of two time ordered fields.