Quantum Weak Energy Inequalities for the Dirac field in Flat Spacetime

Quantum Weak Energy Inequalities (QWEIs) have been established for a variety of quantum field theories in both flat and curved spacetimes. Dirac fields are known (by a result of Fewster and Verch) to satisfy QWEIs under very general circumstances. However this result does not provide an explicit formula for the QWEI bound, so its magnitude has not previously been determined. In this paper we present a new and explicit QWEI bound for Dirac fields of arbitrary mass in four-dimensional Minkowski space. We follow the methods employed by Fewster and Eveson for the scalar field, modified to take account of anticommutation relations. A key ingredient is an identity for Fourier transforms established by Fewster and Verch. We also compare our QWEI with those previously obtained for scalar and spin-1 fields.Comment: 8 pages, REVTeX4, version to appear in Phys Rev

Antiproton-deuteron annihilation at low energies

Recent experimental studies of the antiproton-deuteron system at low energies have shown that the imaginary part of the antiproton-deuteron scattering length is smaller than the antiproton-proton one. Two- and three-body systems with strong annihilation are investigated and a mechanism explaining this unexpected relation between the imaginary parts of the scattering lengths is proposed.Comment: 6 pages, 3 figures, to be published in The European Physical Journal

The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

Stokes-space formalism for Bragg scattering in a fiber

Optical frequency conversion by four-wave mixing (Bragg scattering) in a fiber is considered. The evolution of this process can be modeled using the signal and idler amplitudes, which are complex, or Stokes-like parameters, which are real. The Stokes-space formalism allows one to visualize power and phase information simultaneously, and produces a simple evolution equation for the Stokes parameters

Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g. in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behaviour of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, cross-over regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial.Comment: 15 pages, ReVTEX, no figure

Electromagnetic form factors of light vector mesons

The electromagnetic form factors G_E(q^2), G_M(q^2), and G_Q(q^2), charge radii, magnetic and quadrupole moments, and decay widths of the light vector mesons rho^+, K^{*+} and K^{*0} are calculated in a Lorentz-covariant, Dyson-Schwinger equation based model using algebraic quark propagators that incorporate confinement, asymptotic freedom, and dynamical chiral symmetry breaking, and vector meson Bethe-Salpeter amplitudes closely related to the pseudoscalar amplitudes obtained from phenomenological studies of pi and K mesons. Calculated static properties of vector mesons include the charge radii and magnetic moments: r_{rho+} = 0.61 fm, r_{K*+} = 0.54 fm, and r^2_{K*0} = -0.048 fm^2; mu_{rho+} = 2.69, mu_{K*+} = 2.37, and mu_{K*0} = -0.40. The calculated static limits of the rho-meson form factors are similar to those obtained from light-front quantum mechanical calculations, but begin to differ above q^2 = 1 GeV^2 due to the dynamical evolution of the quark propagators in our approach.Comment: 8 pages of RevTeX, 5 eps figure