Zero and finite temperature Casimir effect of massive vector field between real metals

We consider the Casimir effect of a massive vector field between two semi-infinite dielectric slabs. We first derive the generalization of the Lifshitz formula that gives the Casimir interaction energy of two magnetodielectric slabs separated by a magnetodielectric medium due to the vacuum fluctuations of a massive vector field. We then discuss the asymptotic behaviors of the Casimir energy and the Casimir force in various limits, such as low temperature, high temperature, small mass, large mass, up to the first order in the finite conductivity correction, for two real metal semispaces whose dielectric property is described by the plasma model. Application to the Casimir effect in Randall-Sundrum spacetime is briefly discussed.Comment: 19 page

When renormalizability is not sufficient: Coulomb problem for vector bosons

The Coulomb problem for vector bosons W incorporates a known difficulty; the boson falls on the center. In QED the fermion vacuum polarization produces a barrier at small distances which solves the problem. In a renormalizable SU(2) theory containing vector triplet (W^+,W^-,gamma) and a heavy fermion doublet F with mass M the W^- falls on F^+, to distances r ~ 1/M, where M can be made arbitrary large. To prevent the collapse the theory needs additional light fermions, which switch the ultraviolet behavior of the theory from the asymptotic freedom to the Landau pole. Similar situation can take place in the Standard Model. Thus, the renormalizability of a theory is not sufficient to guarantee a reasonable behavior at small distances for non-perturbative problems, such as a bound state problem.Comment: Four page

A Maximally Symmetric Vector Propagator

We derive the propagator for a massive vector field on a de Sitter background of arbitrary dimension. This propagator is de Sitter invariant and possesses the proper flat spacetime and massless limits. Moreover, the retarded Green's function inferred from it produces the correct classical response to a test source. Our result is expressed in a tensor basis which is convenient for performing quantum field theory computations using dimensional regularization.Comment: 21 pages, no figures, uses LaTeX 2 epsilon, version 2 has an error in eqn (86) corrected and an updated reference lis

Coulomb problem for vector bosons versus Standard Model

The Coulomb problem for vector bosons W(+/-) propagating in an attractive Coulomb field incorporates a known difficulty, i.e. the total charge of the boson localized on the Coulomb center turns out infinite. This fact contradicts the renormalizability of the Standard model, which presumes that at small distances all physical quantities are well defined. The paradox is shown to be resolved by the QED vacuum polarization, which brings in a strong effective repulsion and eradicates the infinite charge of the boson on the Coulomb center. The effect makes the Coulomb problem for vector bosons well defined and consistent with the Standard Model.Comment: 4 page

Charge density of a positively charged vector boson may be negative

The charge density of vector particles, for example W, may change sign. The effect manifests itself even for a free propagation; when the energy of the W-boson is higher than sqrt{2}m and the standing-wave is considered the charge density oscillates in space. The charge density of W also changes sign in close vicinity of a Coulomb center. The dependence of this effect on the g-factor for an arbitrary vector boson, for example rho-meson, is discussed. An origin of this surprising effect is traced to the electric quadrupole moment and spin-orbit interaction of vector particles. Their contributions to the current have a polarization nature. The charge density of this current, rho = -\nabla \cdot P, where P is an effective polarization vector that depends on the quadrupole moment and spin-orbit interaction, oscillates in space, producing zero contribution to the total charge.Comment: 4 pages, revte

Mass for Plasma Photons from Gauge Symmetry Breaking

We derive the effective masses for photons in unmagnetized plasma waves using a quantum field theory with two vector fields (gauge fields). In order to properly define the quantum field degrees of freedom we re-derive the classical wave equations on light-front gauge. This is needed because the usual scalar potential of electromagnetism is, in quantum field theory, not a physical degree of freedom that renders negative energy eigenstates. We also consider a background local fluid metric that allows for a covariant treatment of the problem. The different masses for the longitudinal (plasmon) and transverse photons are in our framework due to the local fluid metric. We apply the mechanism of mass generation by gauge symmetry breaking recently proposed by the authors by giving a non-trivial vacuum-expectation-value to the second vector field (gauge field). The Debye length $\lambda_D$ is interpreted as an effective compactification length and we compute an explicit solution for the large gauge transformations that correspond to the specific mass eigenvalues derived here. Using an usual quantum field theory canonical quantization we obtain the usual results in the literature. Although none of these ingredients are new to physicist, as far as the authors are aware it is the first time that such constructions are applied to Plasma Physics. Also we give a physical interpretation (and realization) for the second vector field in terms of the plasma background in terms of known physical phenomena. Addendum: It is given a short proof that equation (10) is wrong, therefore equations (12-17) are meaningless. The remaining results are correct being generic derivations for nonmagnetized plasmas derived in a covariant QFT framework.Comment: v1: 1+6 pages v2: Several discussions rewritten; Abstract rewritten; References added; v3: includes Addendu

"Square Root" of the Proca Equation: Spin-3/2 Field Equation

New equations describing particles with spin 3/2 are derived. The non-local equation with the unique mass can be considered as "square root" of the Proca equation in the same sense as the Dirac equation is related to the Klein-Gordon-Fock equation. The local equation describes spin 3/2 particles with three mass states. The equations considered involve fields with spin-3/2 and spin-1/2, i.e. multi-spin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and spin projections are obtained. All independent solutions of the local equation are expressed through projection matrices. The first order relativistic wave equation in the 20-dimensional matrix form, the relativistically invariant bilinear form and the corresponding Lagrangian are given. Two parameters characterizing non-minimal electromagnetic interactions of fermions are introduced, and the quantum-mechanical Hamiltonian is found. It is proved that there is only causal propagation of waves in the approach considered.Comment: 17 pages, corrections in Eqs. (50), (51

Casimir effect of electromagnetic field in Randall-Sundrum spacetime

We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.Comment: 20 pages, 4 figure

Exact Solutions of the Duffin Kemmer Petiau Equation for the Deformed Hulthen Potential

Using the Nikiforov Uvarov method, an application of the relativistic Duffin Kemmer Petiau equation in the presence of a deformed Hulthen potential is presented for spin zero particles. We derived the first order coupled differential radial equations which enable the energy eigenvalues as well as the full wavefunctions to be evaluated by using of the Nikiforov Uvarov method that can be written in terms of the hypergeometric polynomials.Comment: 8 pages. submitted to Physica Script

Quantum Corrections to the Reissner-Nordstrom and Kerr-Newman Metrics: Spin 1

A previous evaluation of one-photon loop corrections to the energy-momentum tensor has been extended to particles with unit spin and speculations are presented concerning general properties of such forms.Comment: 21 pages, 1 Figur