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Yang-Mills beta-function from a large-distance expansion of the Schrödinger functional.

Mansfield, P. and Sampaio, M. (1999) 'Yang-Mills beta-function from a large-distance expansion of the Schrödinger functional.', Nuclear physics B., 545 (1-3). pp. 623-655.


For slowly varying fields the Yang-Mills Schrödinger functional can be expanded in terms of local functionals. We show how analyticity in a complex scale parameter enables the Schrödinger functional for arbitrarily varying fields to be reconstructed from this expansion. We also construct the form of the Schrödinger equation that determines the coefficients. Solving this in powers of the coupling reproduces the results of the ‘standard’ perturbative solution of the functional Schrödinger equation which we also describe. In particular the usual result for the beta-function is obtained illustrating how analyticity enables the effects of rapidly varying fields to be computed from the behaviour of slowly varying ones.

Item Type:Article
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Physics Letters B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physics Letters B, 545, 1-3, 19 April 1999, 10.1016/S0550-3213(98)00871-2.
Date accepted:19 September 1998
Date deposited:No date available
Date of first online publication:April 1999
Date first made open access:No date available

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