Quantum versus Classical Dynamics in a driven barrier: the role of kinematic effects

We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. Moreover, in the frequency region of optimal agreement between classical and quantum transmission coefficient, the transmission threshold, i.e. the energy above which the transmission coefficient becomes larger than a specific small threshold value, is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well separated coherent pulses, a phenomenon which can admit purely classical kinematic interpretation

Ring diagrams and electroweak phase transition in a magnetic field

Electroweak phase transition in a magnetic field is investigated within the one-loop and ring diagram contributions to the effective potential in the minimal Standard Model. All fundamental fermions and bosons are included with their actual values of masses and the Higgs boson mass is considered in the range $75 GeV \leq m_H \leq 115 GeV$. The effective potential is real at sufficiently high temperature. The important role of fermions and $W$-bosons in symmetry behaviour is observed. It is found that the phase transition for the field strengths $10^{23} - 10^{24}$G is of first order but the baryogenesis condition is not satisfied. The comparison with the hypermagnetic field case is done.Comment: 16 pages, Latex, changed for a mistake in the numerical par

Laser photon merging in proton-laser collisions

The quantum electrodynamical vacuum polarization effects arising in the collision of a high-energy proton beam and a strong, linearly polarized laser field are investigated. The probability that laser photons merge into one photon by interacting with the proton`s electromagnetic field is calculated taking into account the laser field exactly. Asymptotics of the probability are then derived according to different experimental setups suitable for detecting perturbative and nonperturbative vacuum polarization effects. The experimentally most feasible setup involves the use of a strong optical laser field. It is shown that in this case measurements of the polarization of the outgoing photon and and of its angular distribution provide promising tools to detect these effects for the first time.Comment: 38 pages, 9 figure

Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology

We develop a gauge invariant canonical perturbation scheme for perturbations around symmetry reduced sectors in generally covariant theories, such as general relativity. The central objects of investigation are gauge invariant observables which encode the dynamics of the system. We apply this scheme to perturbations around a homogeneous and isotropic sector (cosmology) of general relativity. The background variables of this homogeneous and isotropic sector are treated fully dynamically which allows us to approximate the observables to arbitrary high order in a self--consistent and fully gauge invariant manner. Methods to compute these observables are given. The question of backreaction effects of inhomogeneities onto a homogeneous and isotropic background can be addressed in this framework. We illustrate the latter by considering homogeneous but anisotropic Bianchi--I cosmologies as perturbations around a homogeneous and isotropic sector.Comment: 39 pages, 1 figur

Chiral and Parity Symmetry Breaking for Planar Fermions: Effects of a Heat Bath and Uniform External Magnetic Field

We study chiral symmetry breaking for relativistic fermions, described by a parity violating Lagrangian in 2+1-dimensions, in the presence of a heat bath and a uniform external magnetic field. Working within their four-component formalism allows for the inclusion of both parity-even and -odd mass terms. Therefore, we can define two types of fermion anti-fermion condensates. For a given value of the magnetic field, there exist two different critical temperatures which would render one of these condensates identically zero, while the other would survive. Our analysis is completely general: it requires no particular simplifying hierarchy among the energy scales involved, namely, bare masses, field strength and temperature. However, we do reproduce some earlier results, obtained or anticipated in literature, corresponding to special kinematical regimes for the parity conserving case. Relating the chiral condensate to the one-loop effective Lagrangian, we also obtain the magnetization and the pair production rate for different fermion species in a uniform electric field through the replacement $B\to-iE$.Comment: 9 pages, 10 figure

From covariant to canonical formulations of discrete gravity

Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits exact gauge symmetries -- we derive local and first class constraints for arbitrary triangulated Cauchy surfaces. These constraints have a clear geometric interpretation and are a first step towards obtaining anomaly--free constraint algebras for canonical lattice gravity. Taking higher order dynamics into account the symmetries of the action are broken. This results in consistency conditions on the background gauge parameters arising from the lowest non--linear equations of motion. In the canonical framework the constraints to quadratic order turn out to depend on the background gauge parameters and are therefore pseudo constraints. These considerations are important for connecting path integral and canonical quantizations of gravity, in particular if one attempts a perturbative expansion.Comment: 37 pages, 5 figures (minor modifications, matches published version + updated references

Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization

The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to the quasi 1D universality class (quantum kicked rotator, "domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.

Magnetic catalysis in QED_3 at finite temperature: beyond the constant mass approximation

We solve the Schwinger-Dyson equations for (2+1)-dimensional QED in the presence of a strong external magnetic field. The calculation is done at finite temperature and the fermionic self energy is not supposed to be momentum-independent, which is the usual simplification in such calculations. The phase diagram in the temperature-magnetic field plane is determined. For intermediate magnetic fields the critical temperature turns out to have a square root dependence on the magnetic field, but for very strong magnetic fields it approaches a B-independent limiting value.Comment: 21 pages, 10 figures, published versio

Emergent diffeomorphism invariance in a discrete loop quantum gravity model

Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory becomes second class upon discretization. If one treats the second class constraints properly, the resulting theories have very different dynamics and number of degrees of freedom than those of the continuum theory. It is therefore questionable how these theories could be considered a starting point for quantization and the definition of a continuum theory through a continuum limit. We show explicitly in a model that the {\em uniform discretizations} approach to the quantization of constrained systems overcomes these difficulties. We consider here a simple diffeomorphism invariant one dimensional model and complete the quantization using {\em uniform discretizations}. The model can be viewed as a spherically symmetric reduction of the well known Husain--Kucha\v{r} model of diffeomorphism invariant theory. We show that the correct quantum continuum limit can be satisfactorily constructed for this model. This opens the possibility of treating 1+1 dimensional dynamical situations of great interest in quantum gravity taking into account the full dynamics of the theory and preserving the space-time covariance at a quantum level.Comment: 12 pages, Revte

A Note on B-observables in Ponzano-Regge 3d Quantum Gravity

We study the insertion and value of metric observables in the (discrete) path integral formulation of the Ponzano-Regge spinfoam model for 3d quantum gravity. In particular, we discuss the length spectrum and the relation between insertion of such B-observables and gauge fixing in the path integral.Comment: 17 page