Conservation laws and stress–energy–momentum tensors for systems with background fields

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress–energy–momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante–Rosenfeld stress–energy–momentum tensor derived from a Noether current and the Einstein–Hilbert stress–energy–momentum tensor derived in the context of Einstein’s theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields.

► The role of background fields in diffeomorphism invariant actions is demonstrated.
► Interrelations between different stress–energy–momentum tensors are emphasised.
► The Abraham and Minkowski electromagnetic tensors are discussed in this context.
► Conservation laws in the presence of nondynamic background fields are formulated.
► The discussion is facilitated by the development of a new variational calculus.