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Fabrizio Palumbo

Publications and source records attributed to Fabrizio Palumbo.

32 records · Page 2Linked to original sources
arXiv2008

Bogoliubov transformations and fermion condensates in lattice field theories

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian.

hep-lat↗
arXiv2007

Composite boson dominance in many-fermion systems

I recently proposed a method of bosonization based on the use of coherent states of fermion composites, whose validity was restricted to smooth structure functions. In the present paper I remove this limitation and derive results which hold for arbitrary interactions and structure functions. The method respects all symmetries and in particular fermion number conservation. It reproduces exactly the results of the pairing model of atomic nuclei and of the BCS model of superconductivity in the number conserving form of the quasi-chemical equilibrium theory.

cond-mat.supr-con↗
arXiv2007

A semi-variational approach to QCD at finite temperature and baryon density

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 at the same time and 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.

hep-lat↗
arXiv2007

Composite boson dominance in relativistic field theories

We apply a new bosonization technique to relativistic field theories of fermions whose partition function is dominated by bosonic composites, and derive the effective action for these bosons. The derivation respects all symmetries, including gauge invariance, with the exception of Euclidean invariance which must be checked a posteriori. We use a lattice regularization which should make applications to gauge theories easier. We test the method on a fermion field theory with quartic interaction in the limit when the number of flavours N_f is large, and show that it reproduces the exact results in the bosonic sector, namely condensation of a compositeboson with the right mass which breaks the discrete chiral invariance of the model. Moreover we determine the structure function of the condensed composite, whose spatial part turns out to be identical to that of the Cooper pairs of the BCS model of superconductivity.

hep-lat↗
arXiv2005

Boson Dominance in nuclei

We present a new method of bosonization of fermion systems applicable when the partition function is dominated by composite bosons. Restricting the partition function to such states we get an euclidean bosonic action from which we derive the Hamiltonian. Such a procedure respects all the fermion symmetries, in particular fermion number conservation, and provides a boson mapping of all fermion operators.

nucl-th↗
arXiv2001

Larger physical volume with a noncompact lattice regularization of SU(N) theories

Recently it has been found that in a noncompact formulation of the SU(2) gauge theory on a lattice the physical volume is larger than in the Wilson theory with the same number of sites. In its original formulation such noncompact regularization is directly applicable to U(N) theories for any N and to SU(N) theories for N=2 only. In this work we extend it to SU(N) for any N and investigate some of its properties.

hep-lat↗
arXiv2001

Noncompact gauge fields on a lattice: SU(n) theories

Recently it has been found that in a noncompact lattice regularization of the SU(2) gauge theory the physical volume is larger than in the Wilson theory with the same number of sites. In its original formulation the noncompact regularization is directly applicable to U(n) theories for any n and to SU(n) theories for n=2. In this paper we extend it to SU(n) for any n and investigate some of its properties.

hep-lat↗
arXiv2000

Lattice QCD and chiral mesons

The standard QCD action is improved by the addition of irrelevant operators built with chiral composites. An effective Lagrangian is derived in terms of auxiliary fields, which has the form of the phenomenological chiral Lagrangians. Our improved QCD action appears promising for numerical simulations as the pion physics is explicitely accounted for by the auxiliary fields.

hep-lat↗
arXiv1999

The quark-composites approach to QCD: The nucleon-pion interaction

We derive the pion-nucleon interaction in the framework of a new perturbative approach to QCD, based on the use of quark composites as fundamental variables. The composites with the quantum numbers of the nucleons are assumed as new integration variables in the Berezin integral which defines the partition function, while the composites with the quantum numbers of the chiral mesons are replaced by auxiliary bosonic fields. The action is modified by the addition of irrelevant operators which provide the kinetic terms for these composites, and the quark action is treated as a perturbation. The resulting expansion has the quark confinement built in. To first order we get the pion-nucleon interaction of the Yukawa model.

hep-lat↗
arXiv1999

Finite temperature QCD in the quark-composites approach

We investigate QCD at finite temperature in the quark composites approach, which is based on the use of quark composites with hadronic quantum numbers as fundamental variables. We find that chiral symmetry restoration and quark deconfinement are one and the same first order phase transition, whose critical temperature, in a one loop approximation, is $T= 2\sqrtΩ ρ^{-2}m_π$, where $m_π$ is the pion mass, $Ω=24$ the number of up and down quark components, and $ρ$ a parameter of order 1 whose precise value can be determined by the study of the pion-pion interaction.

hep-lat↗
arXiv1998

Use of even Grassmann variables to construct effective actions for mesons

A quadratic action in even Grassmann variables with the quantum numbers of the pions has been studied. It includes the $σ$-field in order to be invariant under SU(2)_L times SU(2)_R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined.

hep-lat↗
arXiv1998

A free action for pions as quark composites

In the framework of an approach to bosonization based on the use of fermionic composites as fundamental variables, a quadratic action in even Grassmann variables with the quantum numbers of the pions has been constructed. It includes the sigma-field in order to be invariant under SU(2)_L times SU(2)]_R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. A squared mass for the pions is generated according to PCAC. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined.

hep-ph↗