Chiral symmetry breaking and quark confinement in the nilpotency expansion of QCD

Abstract

We apply to lattice QCD a bosonization method previously developed in which dynamical bosons are generated by time-dependent Bogoliubov transformations. The transformed action can be studied by an expansion in the inverse of the nilpotency index, which is the number of fermionic states in the structure function of composite bosons. When this number diverges the model is solved by the saddle point method which has a variational interpretation. We give a stationary covariant solution for a background matter field whose fluctuations describe mesons. In the saddle point approximations live fermionic quasiparticles with quark quantum numbers which are confined, in the sense that they propagate only in pointlike color singlets. Conditions for chiral symmetry breaking are determined, to be studied numerically, and a derivation of mesons-nucleons action is outlined.

arXiv comment33 pages

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Cited by in corpus (4)

• Diquarks in the nilpotency expansion of QCD and their role at finite chemical potential
• Transfer matrix for Kogut-Susskind fermions in the spin basis
• Absence of sign problem in the (saddle point approximation of the) nilpotency expansion of QCD at finite chemical potential
• Lattice QCD${}_2$ effective action with Bogoliubov transformations