Solutions of Podolsky's Electrodynamics Equation in the First-Order Formalism

The Podolsky generalized electrodynamics with higher derivatives is formulated in the first-order formalism. The first-order relativistic wave equation in the 20-dimensional matrix form is derived. We prove that the matrices of the equation obey the Petiau-Duffin-Kemmer algebra. The Hermitianizing matrix and Lagrangian in the first-order formalism are given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin projections are obtained, and we find the density matrix for the massive state. The $13\times 13$-matrix Schrodinger form of the equation is derived, and the Hamiltonian is obtained. Projection operators extracting the physical eigenvalues of the Hamiltonian are found.Comment: 17 pages, minor corrections, published versio

Bipolaron-SO(5) Non-Fermi Liquid in a Two-channel Anderson Model with Phonon-assisted Hybridizations

We analyze non-Fermi liquid (NFL) properties along a line of critical points in a two-channel Anderson model with phonon-assisted hybridizations. We succeed in identifying hidden nonmagnetic SO(5) degrees of freedom for valence-fluctuation regime and analyze the model on the basis of boundary conformal field theory. We find that the NFL spectra along the critical line, which is the same as those in the two-channel Kondo model, can be alternatively derived by a fusion in the nonmagnetic SO(5) sector. The leading irrelevant operators near the NFL fixed points vary as a function of Coulomb repulsion U; operators in the spin sector dominate for large U, while those in the SO(5) sector do for small U, and we confirm this variation in our numerical renormalization group calculations. As a result, the thermodynamic singularity for small U differs from that of the conventional two-channel Kondo problem. Especially, the impurity contribution to specific heat is proportional to temperature and bipolaron fluctuations, which are coupled electron-phonon fluctuations, diverge logarithmically at low temperatures for small U.Comment: 16 pages, 4 figures, 3 table

Gauge invariance and non-constant gauge couplings

It is shown that space-time dependent gauge couplings do not completely break gauge invariance. We demonstrate this in various gauge theories.Comment: 18 page

Reduction formalism for Dirac fermions on de Sitter spacetime

The reduction formulas for Dirac fermions are derived, using the exact solutions of free Dirac equation on de Sitter spacetime. In the framework of the perturbation theory one studies the Green functions and derive the scatering amplitude in the first orders of perturbation theory.Comment: 12 pages, no figure

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

The Schwinger mechanism and graphene

The Schwinger mechanism, the production of charged particle-antiparticle pairs in a macroscopic external electric field, is derived for 2+1 dimensional theories. The rate of pair production per unit area for four species of massless fermions, with charge $q$, in a constant electric field $E$ is given by $\pi^{-2} \hbar^{-3/2} \tilde{c}^{-1/2} (q E)^{3/2}$ where $\tilde{c}$ is the speed of light for the two-dimensional system. To the extent undoped graphene behaves like the quantum field-theoretic vacuum for massless fermions in 2+1 dimensions, the Schwinger mechanism should be testable experimentally. A possible experimental configuration for this is proposed. Effects due to deviations from this idealized picture of graphene are briefly considered. It is argued that with present day samples of graphene, tests of the Schwinger formula may be possible.Comment: Extensive revisions. The distinction between the vacuum decay rate and the pair production rate in the Schwinger mechanism is now stressed. The discussion of quality of sample needed for a viable experimental test has been significantly expanded. References adde

DRA method: Powerful tool for the calculation of the loop integrals

We review the method of the calculation of multiloop integrals suggested in Ref.\cite{Lee2010}.Comment: 6 pages, contribution to ACAT2011 proceedings, Uxbridge, London, September 5-9, 2011, typos are correcte

Asymptotic Expansions of Feynman Amplitudes in a Generic Covariant Gauge

We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in an unspecified covariant gauge. The complete Mellin representation of such amplitudes is then established in terms of invariants (squared sums of external momenta and squared masses). From the scaling of the invariants by a parameter we extend for the present situation a theorem on asymptotic expansions, previously proven for the case of scalar field theories, valid for both ultraviolet and infrared behaviors of Feynman amplitudes.Comment: 10 pages, revtex, no figure

Some exact properties of the gluon propagator

Recent numerical studies of the gluon propagator in the minimal Landau and Coulomb gauges in space-time dimension 2, 3, and 4 pose a challenge to the Gribov confinement scenario. We prove, without approximation, that for these gauges, the continuum gluon propagator $D(k)$ in SU(N) gauge theory satisfies the bound ${d-1 \over d} {1 \over (2 \pi)^d} \int d^dk {D(k) \over k^2} \leq N$. This holds for Landau gauge, in which case $d$ is the dimension of space-time, and for Coulomb gauge, in which case $d$ is the dimension of ordinary space and $D(k)$ is the instantaneous spatial gluon propagator. This bound implies that $\lim_{k \to 0}k^{d-2} D(k) = 0$, where $D(k)$ is the gluon propagator at momentum $k$, and consequently $D(0) = 0$ in Landau gauge in space-time $d = 2$, and in Coulomb gauge in space dimension $d = 2$, but D(0) may be finite in higher dimension. These results are compatible with numerical studies of the Landau-and Coulomb-gauge propagator. In 4-dimensional space-time a regularization is required, and we also prove an analogous bound on the lattice gluon propagator, ${1 \over d (2 \pi)^d} \int_{- \pi}^{\pi} d^dk {\sum_\mu \cos^2(k_\mu/2) D_{\mu \mu}(k) \over 4 \sum_\lambda \sin^2(k_\lambda/2)} \leq N$. Here we have taken the infinite-volume limit of lattice gauge theory at fixed lattice spacing, and the lattice momentum componant $k_\mu$ is a continuous angle $- \pi \leq k_\mu \leq \pi$. Unexpectedly, this implies a bound on the {\it high-momentum} behavior of the continuum propagator in minimum Landau and Coulomb gauge in 4 space-time dimensions which, moreover, is compatible with the perturbative renormalization group when the theory is asymptotically free.Comment: 13 page

Potentially Large One-loop Corrections to WIMP Annihilation

We compute one-loop corrections to the annihilation of non--relativistic particles $\chi$ due to the exchange of a (gauge or Higgs) boson $\phi$ with mass $\mu$ in the initial state. In the limit $m_\chi \gg \mu$ this leads to the "Sommerfeld enhancement" of the annihilation cross section. However, here we are interested in the case \mu \lsim m_\chi, where the one--loop corrections are well--behaved, but can still be sizable. We find simple and accurate expressions for annihilation from both $S-$ and $P-$wave initial states; they differ from each other if $\mu \neq 0$. In order to apply our results to the calculation of the relic density of Weakly Interacting Massive Particles (WIMPs), we describe how to compute the thermal average of the corrected cross sections. We apply this formalism to scalar and Dirac fermion singlet WIMPs, and show that the corrections are always very small in the former case, but can be very large in the latter. Moreover, in the context of the Minimal Supersymmetric Standard Model, these corrections can decrease the relic density of neutralinos by more than 1%, if the lightest neutralino is a strongly mixed state.Comment: 25 pages, 8 figures. Added an appendix showing that the approximation works well in a scalar toy model. To be published in PRD