2009/07/31 by Tohru Koma · 1 citation
Mathematics · Physics and Astronomy · #Gauge theory #High-Energy Particle Collisions Research #Lattice (music) #Massless particle #Mathematical physics #Nonlinear system #Order (exchange) #Particle physics theoretical and experimental studies #Phase transition #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Sigma #Sigma model #Yang–Mills theory #cond-mat.stat-mech #hep-lat #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.82.034509
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 82(3) (American Physical Society) · 23 pages, no figure, v2: minor corrections; v3: two remarks added at the end of Sec. 4
arxiv created 2010/07/07 · openalex publication_date 2010/08/16 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study lattice SU(2) Yang-Mills theory with dimension d\ensuremath≥4. The model can be expressed as a (d\ensuremath-1)-dimensional O(4) nonlinear \ensuremathσ model in a d-dimensional heat bath. As is well known, the nonlinear \ensuremathσ model alone shows a phase transition. If the quark confinement is a consequence of the absence of a phase transition for the Yang-Mills theory, then the fluctuations of the heat bath must destroy the long-range order of the nonlinear \ensuremathσ model. In order to clarify whether this is true, we replace the fluctuations of the heat bath with Gaussian random variables, and obtain a Langevin equation which yields the effective action of the nonlinear \ensuremathσ model by analyzing the Fokker-Planck equation. It turns out that the fluctuations indeed destroy the long-range order of the nonlinear \ensuremathσ model within a mean-field approximation estimating a critical point, whereas for the corresponding U(1) gauge theory, the phase transition to the massless phase remains against the fluctuations.