Semivariational approach to QCD at finite temperature and baryon density

Abstract

Recently a new bosonization method has been used to derive, at zero fermion density, an effective action for relativistic field theories whose partition function is dominated by fermionic composites, chiral mesons in the case of QCD. This approach shares two important features with variational methods: the restriction to the subspace of the composites, and the determination of their structure functions by a variational calculation. But unlike standard variational methods it treats excited states on the same footing as the ground state.I extend this method including states of nonvanishing fermion (baryon) number and derive an effective action for QCD at finite temperature and baryon density. I test the result on a four-fermion interaction model.

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

“…At zero temperature and chemical potential the first choice minimizes the vacuum energy, but increasing the chemical potential because of Pauli blocking for an increasing number of states we must make the second choice. This is the mechanism for chiral symmetry restoration found in a four-fermion interaction model [5,8], and confirmed for gauge theories in a forthcoming paper [22].…”

“…We expect that by increasing the chemical potential and/or the temperature, an increasing number of components of the background field must be set equal to zero, according to a mechanism observed in the absence of gauge fields [5,8], until chiral symmetry is recovered and color is deconfined. If this expectation is verified, the background field will result in a relevant parameter for the definition of QCD phases in the nilpotency expansion.…”

“…These parameters can then be associated with dynamical bosonic (composite) fields in the presence of fermionic fields (quasiparticles) with the quantum numbers of the bare fermions. A compositeness condition avoids double counting [5]. One thus gets an effective action of composite fields plus quasiparticles, exactly equivalent to the original one, in which ground and excited states can be treated on the same footing.…”

Diquarks in the nilpotency expansion of QCD and their role at finite chemical potential

“…At zero baryon density, D = 0, a variational calculation was performed in [32] and, subsequently, it was recognised to provide the vacuum contribution obtained by a suitable Bogoliubov transformation [45]. Here we sketch the proof of this property in the more general case.…”

Transfer matrix for Kogut-Susskind fermions in the spin basis

“…We became interested in a formulation of the transfer matrix in the spin basis in the framework of relativistic field theories of fermions whose partition function is dominated by bosonic composites [22]. This subject became for us more relevant in the development of an approach to QCD hadronization (meant as the replacement of the QCD degrees of freedom by hadronic ones) that makes use of the operator form of the transfer matrix [23][24][25][26]. Using Kogut-Susskind fermions, because of the lack of a convenient formulation of the transfer matrix, we were able to express our results only in the flavour basis.…”