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Gauge and Integrable Theories in Loop Spaces
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Gauge and Integrable Theories in Loop Spaces
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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.
Forward citations
Cited by 2 Pith papers
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The Hidden Symmetries of Yang-Mills Theory in (1+1)-dimensions
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On the gauge-invariant dynamical charges and densities of the 1-instanton solution
Gauge-invariant charge densities for the 1-instanton are defined via non-Abelian magnetic and electric fluxes through spheres, yielding non-zero values at r=1 for both instanton and anti-instanton.
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