Conserved charges and $L_{\infty }$ algebras

Abstract

We give a formula for conserved charges in an arbitrary Lagrangian field theory expressed in the framework of $L_{\infty }$ algebras. The formula is determined by the theory's $L_{\infty }$ data alone, without reference to the derivative structure of the Lagrangian. Therefore conserved charges can be computed in nonlocal models, such as string field theory, where conventional methods break down. The formula also gives the correct expression for the Hamiltonian of general relativity as a surface integral of the Brown-York stress tensor. Related computations in Yang-Mills theory suggest that spatial boundaries are dealt with in a natural fashion.

32+12 pages, 1 figure; v2: minor improvements