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

Palumbo

2012

Phys. Rev. D

Self Cite

We assume that the most important quark correlations are pairwise at all baryon densities. We introduce correlated pairs by means of Bogoliubov transformations which are functions of time and spatial gauge fields, in the formalism of the transfer matrix with lattice regularization. The dependence on time and gauge fields allows us to enforce gauge invariance and other symmetries term by term in the transformed quantities. The resulting action should be suitable for the description of multiquark mesons and baryons as states of a quark and a diquark. We derive the quark contribution to the free energy at finite chemical potential in a certain approximation. Its expression cannot be evaluated analytically, but it has a definite sign.

“…In the absence of the diquark field, that is whenever D t = 0 for every time t, the background field has already been determined [28]. We outline its derivation.…”

Section: In the Absence Of The Diquark Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Summary and Future Perspectivementioning

confidence: 99%

Section: Time-dependent Bogoliubov Transformationsmentioning

confidence: 99%

“…The trace of the fermion transfer matrix, after the first transformation, was represented in [27,28] as a Berezin integral, with the result…”

Section: Time-dependent Bogoliubov Transformationsmentioning

confidence: 99%

See 3 more Smart Citations

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

Palumbo

2012

Phys. Rev. D

Self Cite

Effective mesonic theory for the ’t Hooft model on the lattice

Pastore

2019

Annals of Physics

Self Cite

We apply to a lattice version of the 't Hooft model, QCD in two space-time dimensions for large number of colours, a method recently proposed to obtain an effective mesonic action starting from the fundamental, fermionic one. The idea is to pass from a canonical, operatorial representation, where the low-energy states have a direct physical interpretation in terms of a Bogoliubov vacuum and its corresponding quasiparticle excitations, to a functional, path integral representation, via the formalism of the transfer matrix. In this way we obtain a lattice effective theory for mesons in a self-consistent setting. We also verify that well-known results from other different approaches are reproduced in the continuum limit.This transformation in canonical, in the sense that it preserves canonical anticommutation relations:where u † J and v † J create, respectively, a particle and an antiparticle in the state J. Canonical coherent states can be defined in the same way:and the resolution of unity reads aŝ2. More on Bogoliubov transformations

Transfer matrix for Kogut-Susskind fermions in the spin basis

Palumbo

2013

Phys. Rev. D

Self Cite

In the absence of interaction it is well known that the Kogut-Susskind regularizations of fermions in the spin and flavor basis are equivalent to each other. In this paper we clarify the difference between the two formulations in the presence of interaction with gauge fields. We then derive an explicit expression of the transfer matrix in the spin basis by a unitary transformation on that one in the flavor basis which is known. The essential key ingredient is the explicit construction of the fermion Fock space for variables which live on blocks. Therefore the transfer matrix generates time translations of two lattice units.Comment: 16 page