On the mass spectrum of the \(2+1\) gauge-Higgs lattice quantum field theory
type: Item
instance of: scholarly article
title: On the mass spectrum of the \(2+1\) gauge-Higgs lattice quantum field theory
zbMATH Open document ID: 0615.58030
DOI: 10.1007/BF01211166
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: We investigate the mass spectrum of a \(2+1\) lattice gauge-Higgs quantum field theory with Wilson action \(\beta A_ p+\lambda A_ H\), where \(A_ p(A_ H)\) is the gauge (gauge-Higgs) interaction. We determine the complete spectrum exactly for all \(\beta,\lambda >0\) by an explicit diagonalization of the gauge invariant ''transfer matrix'' in the approximation that the interaction terms in the spatial directions are omitted; all gauge invariant eigenfunctions are generated directly. For fixed momentum the energy spectrum is pure point and disjoint simple planar loops and strings are energy eigenfunctions. However, depending on the gauge group and Higgs representations, there are bound state energy eigenfunctions not of this form. The approximate model has a rich particle spectrum with level crossings and we expect that it provides an intuitive picture of the number and location of bound states and resonances in the full model for small \(\beta,\lambda >0\). We determine the mass spectrum, obtaining convergent expansions for the first two groups of masses above the vacuum for small \(\beta\),\(\lambda\) and confirm our expectations.
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 81T25
zbMATH DE Number: 3996708
zbMATH Keywords: mass spectrum
zbMATH Keywords: lattice gauge-Higgs quantum field theory
zbMATH Keywords: (gauge-Higgs) interaction
author: Ricardo S. Schor
author: Michael O'Carroll
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3996708