2017/03/31 by R. Leme, O. Oliveira, G. Krein
Mathematics · Physics and Astronomy · #Gauge (firearms) #Gauge theory #Gauss #Lattice (music) #Lattice gauge theory #Markov Chains and Monte Carlo Methods #Markov chain #Monte Carlo method #Quantum Chromodynamics and Particle Interactions #Representation (politics) #Theoretical and Computational Physics #hep-lat
paper · pdf · doi:10.1140/epjc/s10052-018-6101-9
openalex publication_date 2018/08/01 · openalex created_date 2018/08/22 · arxiv created 2018/08/31 · arxiv updated 2018/09/26 · openalex updated_date 2026/08/06
An approximate dual representation for non-Abelian lattice gauge theories in terms of a new set of dynamical variables, the plaquette occupation numbers (PONs) that are natural numbers, is discussed. They are the expansion indices of the local series of the expansion of the Boltzmann factors for every plaquette of the Yang–Mills action. After studying the constraints due to gauge symmetry, the SU(2) gauge theory is solved using Monte Carlo simulations. For a PONs configuration the weight factor is given by Haar-measure integrals over all links whose integrands are products of powers of plaquettes. Herein, updates are limited to changes of the PON at a plaquette or all PONs on a coordinate plane. The Markov chain transition probabilities are computed employing truncated maximal trees and the Metropolis algorithm. The algorithm performance is investigated with different types of updates for the plaquette mean value over a large range of β s. Using a 124 lattice very good agreement with a conventional heath bath algorithm is found for the strong and weak coupling limits. Deviations from the latter being below 0.1% for 2.5< β < 3 . The mass of the lightest JPC=0++ glueball is evaluated and reproduces the results found in the literature.