Generally covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the field momentum does not coincide with the generators of spacetime translations. The reason is traced back to the presence of second class constraints occurring in Dirac theory. Further, it is shown that the modification of the Dirac Lagrangian by a surface term leads to a momentum transfer between the Dirac field and the gravitational background field, resulting in a theory that is free of constraints, but not manifestly hermitian.Comment: final version, to appear in Annals Phy

Sonoluminescence as a QED vacuum effect. II: Finite Volume Effects

In a companion paper [quant-ph/9904013] we have investigated several variations of Schwinger's proposed mechanism for sonoluminescence. We demonstrated that any realistic version of Schwinger's mechanism must depend on extremely rapid (femtosecond) changes in refractive index, and discussed ways in which this might be physically plausible. To keep that discussion tractable, the technical computations in that paper were limited to the case of a homogeneous dielectric medium. In this paper we investigate the additional complications introduced by finite-volume effects. The basic physical scenario remains the same, but we now deal with finite spherical bubbles, and so must decompose the electromagnetic field into Spherical Harmonics and Bessel functions. We demonstrate how to set up the formalism for calculating Bogolubov coefficients in the sudden approximation, and show that we qualitatively retain the results previously obtained using the homogeneous-dielectric (infinite volume) approximation.Comment: 23 pages, LaTeX 209, ReV-TeX 3.2, five figure

Schwinger, Pegg and Barnett approaches and a relationship between angular and Cartesian quantum descriptions II: Phase Spaces

Following the discussion -- in state space language -- presented in a preceding paper, we work on the passage from the phase space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labeled) number of states. With that it is possible to relate an original Schwinger idea to the Pegg and Barnett approach to the phase problem. In phase space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian {\em and} angular coordinates, as limiting elements of the discrete phase space formalism.Comment: Subm. to J. Phys A: Math and Gen. 7 pages, sequel of quant-ph/0108031 (which is to appear on J.Phys A: Math and Gen

A modified Schwinger's formula for the Casimir effect

After briefly reviewing how the (proper-time) Schwinger's formula works for computing the Casimir energy in the case of "scalar electrodynamics" where the boundary conditions are dictated by two perfectly conducting parallel plates with separation "a" in the Z-axis, we propose a slightly modification in the previous approach based on an analytical continuation method. As we will see, for the case at hand our formula does not need the use of Poisson summation to get a (renormalized) finite result.Comment: 6 pages, DFTUZ/93/14 (a short version will appear in the Letters in Math. Phys.

Quantum radiation in external background fields

A canonical formalism is presented which allows for investigations of quantum radiation induced by localized, smooth disturbances of classical background fields by means of a perturbation theory approach. For massless, non-selfinteracting quantum fields at zero temperature we demonstrate that the low-energy part of the spectrum of created particles exhibits a non-thermal character. Applied to QED in varying dielectrics the response theory approach facilitates to study two distinct processes contributing to the production of photons: the squeezing effect due to space-time varying properties of the medium and of the velocity effect due to its motion. The generalization of this approach to finite temperatures as well as the relation to sonoluminescence is indicated.Comment: 20 page

Spontaneous Breaking of Extended Supersymmetry in Global and Local Theories

We review the "no-go" theorems that severely constrain the breaking of N=2 supersymmetry to N=1 (both in rigid supersymmetry and supergravity), and we exhibit some models that evade them.Comment: Contribution to the proceedings of the Spring School and Workshop on String Theory, Gauge Theory and Quantum Gravity, ICTP, Trieste, Italy, March 18-29,1996. Latex file, uses espcrc2.sty and epsf.st

Algebraic structure of the Feynman propagator and a new correspondence for canonical transformations

We investigate the algebraic structure of the Feynman propagator with a general time-dependent quadratic Hamiltonian system. Using the Lie-algebraic technique we obtain a normal-ordered form of the time-evolution operator, and then the propagator is easily derived by a simple ``Integration Within Ordered Product" (IWOP) technique.It is found that this propagator contains a classical generating function which demonstrates a new correspondence between classical and quantum mechanics

Schwinger, Pegg and Barnett and a relationship between angular and Cartesian quantum descriptions

From a development of an original idea due to Schwinger, it is shown that it is possible to recover, from the quantum description of a degree of freedom characterized by a finite number of states (\QTR{it}{i.e}., without classical counterpart) the usual canonical variables of position/momentum \QTR{it}{and} angle/angular momentum, relating, maybe surprisingly, the first as a limit of the later.Comment: 7 pages, revised version, to appear on J. Phys. A: Math and Ge

Bosonic vacuum wave functions from the BCS-type wave function of the ground state of the massless Thirring model

A BCS-type wave function describes the ground state of the massless Thirring model in the chirally broken phase. The massless Thirring model with fermion fields quantized in the chirally broken phase bosonizes to the quantum field theory of the free massless (pseudo)scalar field (Eur. Phys. J. C20, 723 (2001)). The wave functions of the ground state of the free massless (pseudo)scalar field are obtained from the BCS-type wave function by averaging over quantum fluctuations of the Thirring fermion fields. We show that these wave functions are orthogonal, normalized and non-invariant under shifts of the massless (pseudo)scalar field. This testifies the spontaneous breaking of the field-shift symmetry in the quantum field theory of a free massless (pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude calculated for the bosonized BCS-type wave functions coincides with the generating functional of Green functions defined only by the contribution of vibrational modes (Eur. Phys. J. C 24, 653 (2002)) . This confirms the assumption that the bosonized BCS-type wave function is defined by the collective zero-mode (hep-th/0212226). We argue that the obtained result is not a counterexample to the Mermin-Wagner-Hohenberg and Coleman theorems.Comment: 9 pages, Latex, no figures, Revised according to the version accepted for publication in Physics Letters

Quantum Fluctuations of a Coulomb Potential as a Source of Flicker Noise

The power spectrum of quantum fluctuations of the electromagnetic field produced by an elementary particle is determined. It is found that in a wide range of practically important frequencies the power spectrum of fluctuations exhibits an inverse frequency dependence. The magnitude of fluctuations produced by a conducting sample is shown to have a Gaussian distribution around its mean value, and its dependence on the sample geometry is determined. In particular, it is demonstrated that for geometrically similar samples the power spectrum is inversely proportional to the sample volume. It is argued also that the magnitude of fluctuations induced by external electric field is proportional to the field strength squared. A comparison with experimental data on flicker noise measurements in continuous metal films is made.Comment: 11 pages, substantially corrected and extende