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

Mansfield, P.; Sampaio, M.

doi:10.1016/s0550-3213(98)00871-2

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

Mansfield, P.; Sampaio, M.

Authors

P. Mansfield

M. Sampaio

Abstract

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.

Citation

Mansfield, P., & Sampaio, M. (1999). Yang-Mills beta-function from a large-distance expansion of the Schrödinger functional. Nuclear Physics B, 545(1-3), 623-655. https://doi.org/10.1016/s0550-3213%2898%2900871-2

Journal Article Type	Article
Acceptance Date	Sep 19, 1998
Publication Date	Apr 19, 1999
Deposit Date	Jun 16, 2015
Publicly Available Date	Jun 16, 2015
Journal	Nuclear Physics B
Print ISSN	0550-3213
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	545
Issue	1-3
Pages	623-655
DOI	https://doi.org/10.1016/s0550-3213%2898%2900871-2
Related Public URLs	http://arXiv.org/abs/hep-th/9807163