A. L. Mota

CONSISTENCY CONDITIONS FOR 4-D REGULARIZATIONS

From the study of well-known divergent amplitudes we deduce three consistency conditions which are necessary and sufficient to eliminate ambiguities and symmetry violations. The conditions relate divergent integrals of the same degree of divergence and are automatically satisfied within the context of dimensional regularization. We show how the deduced consistency conditions can be satisfied in four-dimensional regularizations. An important conclusion of the present study is the possibility of working with 4-D regularization schemes which preserve the virtues of dimensional regularization avoiding, however, its restrictions.

The Chiral fermion meson model at finite temperature

We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-and-Levy at finite temperature.A modified self-consistent resummation (MSCR) which resums higher order terms in the perturbative expansion is proposed. It is shown that with the MSCR the problem of tachyonic masses is solved, the renormalization of the gap equations is carried out and the Goldstones theorem is verified. We also apply the method to investigate another known case at high temperature and compare with results found in the literature.

The role of hidden ambiguities in the linear sigma model with fermions

Abstract The U L ( 3 ) × U R ( 3 ) linear sigma model (LSM) with quark degrees of freedom is used to show that radiative corrections generate undetermined finite contributions. Their origin is related to surface terms which are differences between divergent integrals with the same degree of divergence. The technique used to detect these ambiguities is an implicit regularization on basic divergent integrals that do not depend on external momenta. We show that such contributions are absorbed by renormalization or fixed by symmetry requirements. The general expression for surface terms is derived. Renormalization group coefficients are calculated, as well as relevant observables for this model, such as f π , f κ and the pion and kaon form factors.

SYMMETRIES AND AMBIGUITIES IN THE LINEAR SIGMA MODEL WITH LIGHT QUARKS

We investigate the role of undetermined finite contributions generated by radiative corrections in an SU(2)×SU(2) linear sigma model with quarks. Although some of such terms can be absorbed in the renormalization procedure, one such contribution is left in the expression for the pion decay constant. This arbitrariness is eliminated by chiral symmetry.

Correlation equalities and upper bounds for the transverse Ising model

Starting from an exact formal identity for the two-state transverse Ising model and using correlation inequalities rigorous upper bounds for the critical temperature and the critical transverse field are obtained which improve effective results.

Temperature effects in a Fermi gas with population imbalance

We investigate temperature effects in a Fermi gas with imbalanced spin populations. From the general expression of the thermal gap equation we find, in {\it weak coupling limit}, an analytical expression for the transition temperature

Superfluidity in two-dimensional imbalanced Fermi gases

T_c

Phase transition in asymmetrical superfluids : Equal Fermi surfaces

as a function of various possibilities of chemical potential and mass asymmetries between the two particle species. For a range of asymmetry between certain specific values, this equation always has two solutions for

Field theoretical approach to electrochemical deposition

T_c

Finite-temperature phase diagram of quasi-two-dimensional imbalanced Fermi gases beyond mean field

which has been interpreted as a reentrant phenomena or a pairing induced by temperature effect. We show that the lower