The Energy-Momentum Tensor(s) in Classical Gauge Theories

Abstract

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. The relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.

34 pages; v2: Slightly expanded version with some improvements of presentation; Contribution to Mathematical Foundations of Quantum Field Theory, special issue in memory of Raymond Stora, Nucl. Phys. B