Asymptotic Conservation Laws in Classical Field Theory

Abstract

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms.The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the ADM energy in general relativity.

Boundary charges in gauge theories: using Stokes theorem in the bulk

“…Recent results from variational calculus [6] (see [7] for a review and also [8,9]) corroborate this point of view:…”

“…In [11], it has been pointed out that using the Killing equationD µξµ +D νξν = 0, the corresponding expression in the linearized theory agrees with the simplified expression given in equation (11) of [8]. Accordingly, in the full theory, using the Killing equation…”

“…This leaves of course a lot of freedom in the definition of these forms, and allows one to show for instance that the expressions derived in [12,1,2,8] for energy-momentum and angular momentum in asymptotically flat general relativity are all equivalent (see also e.g. [13] for a recent discussion).…”

“…The n−2 formskf [ϕ;φ] have been explicitly computed in [11] for Yang-Mills theory and Einstein gravity with cosmological constant and the results of [2,3] and [8] have been recovered. From the point of view of [2,3] the contracting homotopy ρ p H,ϕ provides a systematic way of converting "volume integrals to surface integrals".…”

Noether Currents for Bosonic Branes

“…For the interested reader, this subject and its consequences on the global structure of the space of solutions of a relativistic theory is developed in detail e.g. by Anderson and Torre in [28,29,30]. This paper is organized as follows.…”