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

Mansfield, P.; Sampaio, M.

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
• Electronic ISSN: 1873-1562
• 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
• Public URL: https://durham-repository.worktribe.com/output/1598601
• Related Public URLs: http://arXiv.org/abs/hep-th/9807163