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

Mansfield, Paul

Authors

Paul Mansfield



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.