Transition amplitude, partition function and the role of physical degrees of freedom in gauge theories

This work explores the quantum dynamics of the interaction between scalar (matter) and vectorial (intermediate) particles and studies their thermodynamic equilibrium in the grand-canonical ensemble. The aim of the article is to clarify the connection between the physical degrees of freedom of a theory in both the quantization process and the description of the thermodynamic equilibrium, in which we see an intimate connection between physical degrees of freedom, Gibbs free energy and the equipartition theorem. We have split the work into two sections. First, we analyze the quantum interaction in the context of the generalized scalar Duffin-Kemmer-Petiau quantum electrodynamics (GSDKP) by using the functional formalism. We build the Hamiltonian structure following the Dirac methodology, apply the Faddeev-Senjanovic procedure to obtain the transition amplitude in the generalized Coulomb gauge and, finally, use the Faddeev-Popov-DeWitt method to write the amplitude in covariant form in the no-mixing gauge. Subsequently, we exclusively use the Matsubara-Fradkin (MF) formalism in order to describe fields in thermodynamical equilibrium. The corresponding equations in thermodynamic equilibrium for the scalar, vectorial and ghost sectors are explicitly constructed from which the extraction of the partition function is straightforward. It is in the construction of the vectorial sector that the emergence and importance of the ghost fields are revealed: they eliminate the extra non-physical degrees of freedom of the vectorial sector thus maintaining the physical degrees of freedom

On the Integrability and Chaos of an N=2 Maxwell-Chern-Simons-Higgs Mechanical Model

We apply different integrability analysis procedures to a reduced (spatially homogeneous) mechanical system derived from an off-shell non-minimally coupled N=2 Maxwell-Chern-Simons-Higgs model that presents BPS topological vortex excitations, numerically obtained with an ansatz adopted in a special - critical coupling - parametric regime. As a counterpart of the regularity associated to the static soliton-like solution, we investigate the possibility of chaotic dynamics in the evolution of the spatially homogeneous reduced system, descendant from the full N=2 model under consideration. The originally rich content of symmetries and interactions, N=2 susy and non-minimal coupling, singles out the proposed model as an interesting framework for the investigation of the role played by (super-)symmetries and parametric domains in the triggering/control of chaotic behavior in gauge systems. After writing down effective Lagrangian and Hamiltonian functions, and establishing the corresponding canonical Hamilton equations, we apply global integrability Noether point symmetries and Painleveproperty criteria to both the general and the critical coupling regimes. As a non-integrable character is detected by the pair of analytical criteria applied, we perform suitable numerical simulations, as we seek for chaotic patterns in the system evolution. Finally, we present some Comments on the results and perspectives for further investigations and forthcoming communications.Comment: 18 pages, 5 figure

Ordenha higiênica de leite de cabra.

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N=2-Maxwell-Chern-Simons model with anomalous magnetic moment coupling via dimensional reduction

An N=1--supersymmetric version of the Cremmer-Scherk-Kalb-Ramond model with non-minimal coupling to matter is built up both in terms of superfields and in a component-field formalism. By adopting a dimensional reduction procedure, the N=2--D=3 counterpart of the model comes out, with two main features: a genuine (diagonal) Chern-Simons term and an anomalous magnetic moment coupling between matter and the gauge potential.Comment: 15 pages, Latex; one reference corrected; To be published in the Int. J. Mod. Phys.

Self-dual vortices in a Maxwell-Chern-Simons model with non-minimal coupling

We find self-dual vortex solutions in a Maxwell-Chern-Simons model with anomalous magnetic moment. From a recently developed N=2-supersymmetric extension, we obtain the proper Bogomol'nyi equations together with a Higgs potential allowing both topological and non-topological phases in the theory.Comment: 12 pages, 9 figures, 2 tables; some typos corrected, one reference updated. To be published in the Int. J. Mod. Phys. A (1999

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Interference and complementarity for two-photon hybrid entangled states

In this work we generate two-photon hybrid entangled states (HES), where the polarization of one photon is entangled with the transverse spatial degree of freedom of the second photon. The photon pair is created by parametric down-conversion in a polarization-entangled state. A birefringent double-slit couples the polarization and spatial degrees of freedom of these photons and finally, suitable spatial and polarization projections generate the HES. We investigate some interesting aspects of the two-photon hybrid interference, and present this study in the context of the complementarity relation that exists between the visibilities of the one- and two-photon interference patterns.Comment: 10 pages, 4 figures. Accepted in Physical Review