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

1998/07/21 by Paul Mansfield, Marcos Sampaio · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th

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

published as Nucl.Phys. B545 (1999) 623-655 · 31 pages, LaTeX, 5 figures

arxiv created 1998/07/21 · openalex publication_date 1999/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For slowly varying fields the Yang-Mills Schroedinger functional can be expanded in terms of local functionals. We show how analyticity in a complex scale parameter enables the Schroedinger functional for arbitrarily varying fields to be reconstructed from this expansion. We also construct the form of the Schroedinger equation that determines the coefficients. Solving this in powers of the coupling reproduces the results of the `standard' perturbative solution of the functional Schroedinger 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.

Citations

• Schrödinger Representation in Renormalizable Quantum Field Theory
• The Schrödinger functional — a renormalizable probe for non-abelian gauge theories

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