Gauge and Integrable Theories in Loop Spaces

Abstract

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of an hyper-volume ordered integral to an hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories.

36 pages, 6 figures, references added

References in corpus (3)

• Integrable theories and loop spaces: fundamentals, applications and new developments
• A simple formula for the conserved charges of soliton theories
• An integral formulation of Yang-Mills on loop space

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