Y. Brihaye

Vector mesons within the effective Lagrangian approach

Abstract We construct an effective lagrangian which describes the non-anomalous and the anomalous interactions between the low-lying pseudoscalar mesons and their vector and axial vector partners. By first observing that the approximate non-abelian gauging of the Wess-Zumino-Witten action does not reproduce the purely pionic and electromagnetic low-energy theorems through the vector-meson dominance, we develop a systematic functional subtraction formalism to implement the vector meson dominance unambiguously. This enables us to construct the unique effective π V and π VA actions which reproduce all the low-energy theorems exactly without any constraints on the fundamental parameters of the model.

The weak-coupling phase of lattice spin and gauge models

We analyze the lattice weak-coupling (w.c.) expansion of O(N), CPN−1 and chiral spin models, and of large-N reduced chiral and gauge models. n nWe find that the w.c. expansion always agrees with mean field results, whenever comparable, for arbitrary space-time dimensions, and that the expansion of the reduced models agrees with that of the original ones. However, w.c. results disagree with one-dimensional large-N and (old and new) exact results. We explain this phenomenon as a failure of the analytic continuation from higher dimensions that defines lattice w.c. perturbation theory for massless models (even if infrared singularities always cancel). n nWe use an improved version of the mean field (m.f.) technique suitable for reduced models. We compute the m.f. approximation of chiral models and use this result to determine the large-d (m.f.) behaviour of reduced gauge models, finding agreement with standard Wilson theory results. n nWe give a new characterization of large-N chiral models in terms of the single-link integral for the adjoint representation of SU(N).

Construction of the Effective Vertices and the Gauge Invariant Currents in the Gauged {Wess-Zumino} Action

Abstract The vector flavour current is derived directly from the recently proposed gauged Wess-Zumino action. This gauge covariant expression is used to compute the baryonic and electromagnetic currents. We perform a small field expansion of the pure vector Wess-Zumino action and present the first few terms in a gauge invariant form. Special attention is paid to the two flavour action; in the electromagnetic and the vector-axial vector cases, the results are presented in a manifestly gauge invariant form in terms of the physical pion field.

Sphalerons and normal modes in the (1 + 1)-dimensional abelian Higgs model on the circle

Abstract The abelian Higgs model is considered on the circle. The periodic sphaleron solutions are constructed explicitly. The equations for the normal modes about these solutions resemble Lame equations. For special values of the Higgs field mass a number of modes are obtained analytically, including in particular the negative modes.

QUASI-EXACTLY SOLVABLE RADIAL DIRAC EQUATIONS

In the background of a central Coulomb potential, the Schrodinger and Dirac equations lead to exactly solvable spectral problems. When the Schrodinger–Coulomb equation is supplemented by a Harmonic potential, the corresponding spectral problem still possesses a finite number of algebraic solutions: it is quasi-exactly solvable. In this letter we analyze the spectral problem corresponding to the Dirac–Coulomb problem supplemented by a linear radial potential and we show that it also leads to quasi-exactly solvable equations.

CENTRAL POTENTIALS AND EXAMPLES OF HIDDEN ALGEBRA STRUCTURE

We propose two generalizations of the Coulomb potential equation of quantum mechanics and investigate the occurrence of algebraic eigenfunctions for the corresponding Schrodinger equations. Some relativistic counterparts of these problems are also discussed.We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrhodinger equations. Some relativistic counterparts of these problems are also discussed.

The continuum limit of one-dimensional non-linear models

Group invariant expectation values for lattice non-linear vector models [O(N) and CPN−1] in one dimension with a general local action may be expressed as explicit functions of the single-link model expectation values. The value of all these averages at the fixed point of the renormalization group can be determined exactly, in such a way that the continuum expectation values are generated. The large N limit and the reconstruction of the fixed point lattice action are discussed.

Minimizing configurations of the action in the twisted Eguchi-Kawai model

Abstract We obtain the most general twist matrix compatible with the minimization condition of the twisted Eguchi-Kawai model. For all values of the twist tensor, we propose configurations of matrices which realize the minimum of the action.

Schwinger-Dyson equations in reduced twisted chiral models

Abstract We have shown that the Schwinger-Dyson equations for the original (infinite volume) chiral model on the lattice and the reduced, twisted chiral model are equivalent in the large N limit. Our derivation is valid in any even dimension of space-time and does not depend on the coupling constant. Only a discrete symmetry, which is not broken, is invoked to establish the correspondence.

The twisted Eguchi-Kawai model fails to reproduce the weak coupling of the wilson model

Abstract We perform a saddle point analysis of the twisted Eguchi-Kawai model in two, three and four dimensions. Our conclusion is that this model does not reproduce the usual Wilson model results in the weak coupling region at the large N limit. However, we stress that the deviations between the two models are small and decrease with increasing dimension of space.