Solving the functional Schrödinger equation: Yang-Mills string tension and surface critical scaling

Mansfield, Paul

Abstract

Motivated by a heuristic model of the Yang-Mills vacuum that accurately describes the string-tension in three dimensions we develop a systematic method for solving the functional Schrödinger equation in a derivative expansion. This is applied to the Landau-Ginzburg theory that describes surface critical scaling in the Ising model. A Renormalisation Group analysis of the solution yields the value η = 1.003 for the anomalous dimension of the correlation function of surface spins which compares well with the exact result of unity implied by Onsager's solution. We give the expansion of the corresponding β-function to 17-th order (which receives contributions from up to 17-loops in conventional perturbation theory).

Citation

Mansfield, P. (2004). Solving the functional Schrödinger equation: Yang-Mills string tension and surface critical scaling. Journal of High Energy Physics, 2004(04), https://doi.org/10.1088/1126-6708/2004/04/059

• Journal Article Type: Article
• Acceptance Date: Apr 23, 2004
• Online Publication Date: Apr 1, 2004
• Publication Date: Apr 23, 2004
• Deposit Date: Mar 26, 2008
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2004
• Issue: 04
• DOI: https://doi.org/10.1088/1126-6708/2004/04/059
• Keywords: Renormalization group, Field theories in lower dimensions, Confinement, Boundary quantum field theory.
• Public URL: https://durham-repository.worktribe.com/output/1598663