Document Zbl 1041.81083

A formulation of the Yang-Mills theory as a deformation of a topological field theory based on the background field method and quark confinement problem. (English) Zbl 1041.81083

Int. J. Mod. Phys. A 16, No. 7, 1303-1346 (2001).

During the past twenty years, several authors have proposed various strategies to develop a theory that incorporates quark confinement in quantum chromodynamics (QCD). One of the more recent attempts, in this regard, has been undertaken by the author of the article under review. In 1998 he had proposed a new formulation of a Yang-Mills theory that appeared as a (perturbative) deformation theory within topological quantum field theory. In his approach, quark confinement in QCD could be derived at least in the maximal Abelian gauge.
Now, in the present paper, the author re-derives his previous formulation of a Yang-Mills theory in another framework namely by using the so-called background field method (BGFM). This new formulation turns out to be utmost suitable for the description of various scenarios of quark confinement, sheds some more light on the topological theory of solitons, helps to simplify many proofs in this context, and leads to a method of numerical simulation to confirm the validity of the author’s general approach to Yang-Mills theory. Finally it is pointed out that the gauge fixing part of this approach seems to have a geometric meaning from the view-point of global topology.
Altogether, this paper represents a major contribution of high strategical value to the subject of physical Yang-Mills theory.

Reviewer: Werner Kleinert (Berlin)

Cited in 1 Document

MSC:

81T13	Yang-Mills and other gauge theories in quantum field theory
81T45	Topological field theories in quantum mechanics
58E15	Variational problems concerning extremal problems in several variables; Yang-Mills functionals

Keywords:

topological quantum field theory; magnetic monopole; topological soliton; instanton calculus; quantum chromodynamics; background field method

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