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Itô calculus for σ-models and Yang-Mills theories

✍ Scribed by A. Patrascioiu; J. L. Richard

Publisher
Springer
Year
1985
Tongue
English
Weight
150 KB
Volume
9
Category
Article
ISSN
0377-9017

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✦ Synopsis

It is pointed out that the effective continuum action for a-models and Yang-Mills theories may differ from the naive continuum action by terms of order g2 or higher, which are nonsymmetric. The modifications are produced by a generalization of the It6 calculus to dimensions higher than one.

Consider a nonrelativistic particle free to move on a sphere S 2 (H = L2/2MR2). It can be verified [ 1 ] that the Feynman-Kac formula for the propagator is given by

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