A new look at the problem of gauge invariance in quantum field theory

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.Comment: Accepted by Physica Scripta. 27 page

Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal

We study the dynamics of the 2+1 Dirac oscillator exactly and find spin oscillations due to a {\it Zitterbewegung} of purely relativistic origin. We find an exact mapping of this quantum-relativistic system onto a Jaynes-Cummings model, describing the interaction of a two-level atom with a quantized single-mode field. This equivalence allows us to map a series of quantum optical phenomena onto the relativistic oscillator, and viceversa. We make a realistic experimental proposal, at reach with current technology, for studying the equivalence of both models using a single trapped ion.Comment: Revtex4, submitted for publicatio

Conditions driving chemical freeze-out

We propose the entropy density as the thermodynamic condition driving best the chemical freeze-out in heavy-ion collisions. Taking its value from lattice calculations at zero chemical potential, we find that it is excellent in reproducing the experimentally estimated freeze-out parameters. The two characteristic endpoints in the freeze-out diagram are reproduced as well.Comment: 8 pages, 5 eps figure

About the Dirac Equation with a δ\delta potential

An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the occurrence of supercritical effects.Comment: 8 pages, 1 postscript figure, Latex, Revise

Proof that the Hydrogen-antihydrogen Molecule is Unstable

In the framework of nonrelativistic quantum mechanics we derive a necessary condition for four Coulomb charges $(m_{1}^+, m_{2}^-, m_{3}^+, m_{4}^-)$, where all masses are assumed finite, to form the stable system. The obtained stability condition is physical and is expressed through the required minimal ratio of Jacobi masses. In particular this provides the rigorous proof that the hydrogen-antihydrogen molecule is unstable. This is the first result of this sort for four particles.Comment: Submitted to Phys.Rev.Let

A New Study of the Transition to Uniform Nuclear Matter in Neutron Stars and Supernovae

A comprehensive microscopic study of the properties of bulk matter at densities just below nuclear saturation $\rho_s = 2.5 \sim 10^{14}$ g cm$^{-3}$, zero and finite temperature and high neutron fraction, is outlined, and preliminary results presented. Such matter is expected to exist in the inner crust of neutron stars and during the core collapse of massive stars with $M \gtrsim 8M_{\odot}Comment: 4 pages, 2 figures. Participant Contribution at the ``Dense Matter in Heavy Ion Collisions and Astrophysics" Summer School, JINR, Dubna, Aug. 21 - Sept. 1, 2006. To be published in PEPAN letter

Color plasma oscillation in strangelets

The dispersion relation and damping rate of longitudinal color plasmons in finite strange quark matter (strangelets) are evaluated in the limits of weak coupling, low temperature, and long wavelength. The property of the QCD vacuum surrounding a strangelet makes the frequency of the plasmons nearly the same as the color plasma frequency of bulk matter. The plasmons are damped by their coupling with individual excitations of particle-hole pairs of quarks, of which the energy levels are discretized by the boundary. For strangelets of macroscopic size, the lifetime of the plasmons is found to be proportional to the size, as in the case of the usual plasma oscillations in metal nanoparticles.Comment: 9 pages (REVTeX), 2 Postscript figures, to be published in Phys. Rev.

Non-locality of Foldy-Wouthuysen and related transformations for the Dirac equation

Non-localities of Foldy-Wouthuysen and related transformations, which are used to separate positive and negative energy states in the Dirac equation, are investigated. Second moments of functional kernels generated by the transformations are calculated, the transformed functions and their variances are computed. It is shown that all the transformed quantities are smeared in the coordinate space by the amount comparable to the Compton wavelength $\lambda_c=\hbar/mc$.Comment: 7 pages, two figure

Field-induced decay of quantum vacuum: visualizing pair production in a classical photonic system

The phenomenon of vacuum decay, i.e. electron-positron pair production due to the instability of the quantum electrodynamics vacuum in an external field, is a remarkable prediction of Dirac theory whose experimental observation is still lacking. Here a classic wave optics analogue of vacuum decay, based on light propagation in curved waveguide superlattices, is proposed. Our photonic analogue enables a simple and experimentally-accessible visualization in space of the process of pair production as break up of an initially negative-energy Gaussian wave packet, representing an electron in the Dirac sea, under the influence of an oscillating electric field