The O(N) σ-model Laplacian

1995/11/06 by Paul Mansfield, Jiannis K. Pachos, Jiannis Pachos
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geology #Quantum chaos and dynamical systems #hep-th

paper · pdf · doi:10.1016/0370-2693(95)01333-4

published as Phys.Lett. B365 (1996) 169-174 · 7 pages, latex

arxiv created 1995/11/06 · openalex publication_date 1996/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional of a massive quantum field theory can be expanded in terms of local functionals satisfying a form of the Schrödinger equation, the principal ingredient of which is a regulated functional Laplacian. We construct to leading order a Laplacian for the O(N) sigma-model that acts on such local functionals. It is determined by imposing rotational invariance in the internal space together with closure of the Poincaré algebra.

Citations

• Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery
• Quantum field theories on manifolds with curved boundaries: Scalar fields
• Schrödinger representation and Casimir effect in renormalizable quantum field theory
• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories