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

2000/09/15 by Dirk Prange, Prange, Dirk
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/0009124

94 pages, doctoral thesis

arxiv created 2000/09/15 · arxiv updated 2009/11/30

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 phi⁴-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.

Related

• Gauge theories in local causal perturbation theory
• Perturbative QFT: off-shell fields, deformation quantization and causal perturbation theory
• Functional Formalism for Algebraic Classical and Quantum Field Theories
• The Operator Product Expansion in Quantum Field Theory
• Conservation Law and Trace Anomaly for the Stress Energy Tensor of a Self-Interacting Scalar Field