8,974 research outputs found

    A Theory of the Casimir Effect for Compact Regions

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    We develop a mathematically precise framework for the Casimir effect. Our working hypothesis, verified in the case of parallel plates, is that only the regularization-independent Ramanujan sum of a given asymptotic series contributes to the Casimir pressure. As an illustration, we treat two cases: parallel plates, identifying a previous cutoff free version (by G. Scharf and W. W.) as a special case, and the sphere.We finally discuss the open problem of the Casimir force for the cube. We propose an Ansatz for the exterior force and argue why it may provide the exact solution, as well as an explanation of the repulsive sign of the force.Comment: version published, 23 page

    Causal Theory for the Gauged Thirring Model

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    We consider the (2+1)-dimensional massive Thirring model as a gauge theory, with one fermion flavor, in the framework of the causal perturbation theory and address the problem of dynamical mass generation for the gauge boson. In this context we get an unambiguous expression for the coefficient of the induced Chern-Simons term.Comment: LaTex, 21 pages, no figure

    Radiative Corrections for the Gauged Thirring Model in Causal Perturbation Theory

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    We evaluate the one-loop fermion self-energy for the gauged Thirring model in (2+1) dimensions, with one massive fermion flavor, in the framework of the causal perturbation theory. In contrast to QED3_3, the corresponding two-point function turns out to be infrared finite on the mass shell. Then, by means of a Ward identity, we derive the on-shell vertex correction and discuss the role played by causality for nonrenormalizable theories.Comment: LaTex, 09 pages, no figures. Title changed and introduction enlarged. To be published in Eur. Phys. J.

    Distributional approach to point interactions in one-dimensional quantum mechanics

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    We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schr\"odinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called δ′\delta^\prime interaction.Comment: Open Access link: http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/abstrac

    Gauged Thirring Model in the Heisenberg Picture

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    We consider the (2+1)-dimensional gauged Thirring model in the Heisenberg picture. In this context we evaluate the vacuum polarization tensor as well as the corrected gauge boson propagator and address the issues of generation of mass and dynamics for the gauge boson (in the limits of QED3_3 and Thirring model as a gauge theory, respectively) due to the radiative corrections.Comment: 14 pages, LaTex, no figure

    Relativistic Tunneling Through Two Successive Barriers

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    We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called \emph{Generalized Hartman Effect}, an effect observed in the context of nonrelativistic tunneling as well as in its electromagnetic counterparts, and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows the emergence of the Generalized Hartman Effect. We compare our results with the nonrelativistic ones and discuss their interpretation.Comment: 7 pages, 3 figures. Revised version, with a new appendix added. Slightly changes in the styles and captions of Figures 1 and 2. To appear in Physical Review
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