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Title: Reformulations of the Yang-Mills theory toward quark confinement and mass gap

We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N− 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1){supmore » N−1}, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.« less
Authors:
;  [1] ;  [2] ;  [3]
  1. Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522 (Japan)
  2. Fukui National College of Technology, Sabae 916-8507 (Japan)
  3. Computing Research Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan)
Publication Date:
OSTI Identifier:
22499026
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1701; Journal Issue: 1; Conference: 11. conference on quark confinement and hadron spectrum, Saint Petersburg (Russian Federation), 8-12 Sep 2014; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BAG MODEL; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CONFINEMENT; GAUGE INVARIANCE; MAGNETIC MONOPOLES; MASS; SCALAR FIELDS; STABILITY; SUPERCONDUCTIVITY; WILSON LOOP; YANG-MILLS THEORY