A. Barducci

Supersymmetries and the pseudoclassical relativistic electron

SummaryIn this work we consider a version of the supersymmetry parametrized by anticommuting pseudovector and pseudoscalar variables instead of spinorial ones. We construct a pseudoclassical relativistic Lagrangian invariant under the former supersymmetry. This Lagrangian is a degenerate one and we show that, after quantization, one of the constraints gives rise to the Dirac equation. Moreover, we introduce into our Lagrangian an interaction term with an external electromagnetic field, and we show that this is possible, in a consistent way, only if the anomalous magnetic moment is vanishing. It follows that this model represents a pseudoclassical description for the relativistic electron.RiassuntoIn questo lavoro si considera una versione della supersimmetria la cui parametrizzazione è effettuata in termini di variabili anticommutanti pseudovettoriali e pseudoscalari invece che spinoriali. Si costruisce una Lagrangiana relativistica pseudoclassica invariante rispetto alla precedente supersimmetria. Questa Lagrangiana risulta degenere e si mostra che, dopo quantizzazione, uno dei vincoli dà luogo alla equazione di Dirac. Nella nostra Lagrangiana si introduce inoltre un termine di interazione con un campo elettromagnetico esterno, e si mostra che ciò è possibile in maniera consistente solo se il momento magnetico anomalo è nullo. Segue che questo modello rappresenta una descrizione pseudoclassica per l’elettrone relativistico.РеэюмеВ зтой работе мы рассматриваем вариант суперсимметрии, пара-метриэованной с помошью антикоммутирующих псевдовекторБых и псевдоскаляр-ных переменных, вместо спинорных переменных. Мы конструируем псевдокласси-ческий релятивистский Лагранжиан, инвариантный относительно первой иэ выщеу-каэанных суперсимметрий. Этот Лагранжиан является вырожденным и мы по-каэываем, что после квантования одно иэ ограничений приводит к уравнению Ди-рака. Кроме того, мы вводим в нащ Лагранжиан член вэаимодействия с внещним злектромагнитным полем. Мы покаэываем, что зто воэможно сделать непротиво-речивым обраэом, если только аномальный магнитный момент обрашается в нуль. Иэ зтого следует, что предложенная модель представляет псевдоскалярное описание для релятивистского злектрона.

Classical scalar and spinning particles interacting with external Yang-Mills fields

Abstract We derive the classical equations of motion for scalar and spinning particles interacting with an external Yang-Mills field. The internal degrees of freedom are described by a set of Grassmann variables; in this way, after quantization, we get automatically finite-dimensional representations of the internal symmetry group. By requiring that the Lagrangian is gauge invariant we determine the general form for the coupling terms. In particular we obtain a generalized version of the Bargmann-Michel-Telegdi equation, which is valid for a spin - 1 2 particle in an arbitrary external field.

Chiral-symmetry breaking in QCD at finite temperature and density

Abstract We make a theoretical study of chiral symmetry breaking for a QCD-like gauge theory at finite temperature and density. We use a composite-operator functional formalism based on an effective action extending previous calculations for zero temperature and density. Study of the phase diagram shows the existence on the critical line of a point separating second order from first order phase transitions.

Classical spinning particles interacting with external gravitational fields

Abstract In this paper we study the coupling between the pseudoclassical spinning particle and an arbitrary gravitational field. The gravitational field is treated as a gauge field in order to deal with possible contributions from the torsion of space-time. We find that the spinning particle cannot be coupled directly to the torsion. We study the classical equations of motion which turn out to be the same as derived by Papapetrou in order to describe the so called pole-dipole singularity in general relativity. We discuss also the structure of the energy-momentum tensor for the spinning particle.

Calculation of the QCD phase diagram at finite temperature, and baryon and isospin chemical potentials

We study the phases of a two-flavor Nambu\char21{}Jona-Lasinio model at finite temperature T, and baryon and isospin chemical potentials

Heuristic Argument for Coincidence or Almost Coincidence of Deconfinement and Chirality Restoration in Finite Temperature {QCD}

{\ensuremath{\mu}}_{B}=({\ensuremath{\mu}}_{u}+{\ensuremath{\mu}}_{d})/2,

Anticommuting variables, internal degrees of freedom, and the Wilson loop

{\ensuremath{\mu}}_{I}=({\ensuremath{\mu}}_{u}\ensuremath{-}{\ensuremath{\mu}}_{d})/2.

Path integral quantization of spinning particles interacting with crossed external electromagnetic fields

This study completes a previous analysis where only small isospin chemical potentials

Ladder-QCD at finite isospin chemical potential

{\ensuremath{\mu}}_{I}