Renormalization and asymptotic expansion of Dirac's polarized vacuum

We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no `real' electron. We show that it admits an asymptotic expansion to any order in powers of the physical coupling constant \alphaph, provided that the ultraviolet cut-off behaves as \Lambda\sim e^{3\pi(1-Z_3)/2\alphaph}\gg1. The renormalization parameter $

Duality-invariant Quantum Field Theories of Charges and Monopoles

We present a manifestly Lorentz- and SO(2)-Duality-invariant local Quantum Field Theory of electric charges, Dirac magnetic monopoles and dyons. The manifest invariances are achieved by means of the PST-mechanism. The dynamics for classical point particles is described by an action functional living on a circle, if the Dirac-Schwinger quantization condition for electric and magnetic charges holds. The inconsistent classical field theory depends on an arbitrary, but fixed, external vector field, a generalization of the Dirac-string. Nevertheless, the Quantum Field Theory, obtained from this classical action via a functional integral approach, turns out to be independent of the particular vector field chosen, and thus consistent, if the Dirac-Schwinger quantization condition holds. We provide explicit expressions for the generating functionals of observables, proving that they are Dirac-string independent. Since Lorentz-invariance is manifest at each step, the quantum theory admits also a manifestly diffeomorphism invariant coupling to external gravity. Relations with previous formulations, and with SO(2)--non invariant theories are clarified.Comment: 49 pages, LaTeX, no figure

Variational principle and energy-momentum tensor for relativistic Electrodynamics of point charges

We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz-Dirac equations for the particles and entails, via Noether theorem, this energy-momentum tensor. Our action is obtained from the standard action for classical Electrodynamics, by means of a new Lorentz-invariant regularization procedure, followed by a renormalization. The method introduced here extends naturally to charged p-branes and arbitrary dimensions.Comment: 36 pages, no figures, refs. and comments adde

Nonrelativistic anyons in external electromagnetic field

The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic fields. Consistent coupling of the underlying classical system to arbitrary fields is introduced; at a critical value of the magnetic field, the particle follows a Hall-like law of motion. The corresponding quantized system reveals a hidden nonlocality if the magnetic field is inhomogeneous. In the quantum Landau problem spectral as well as state structure (finite vs. infinite) asymmetry is found. The bound and scattering states, separated by the critical magnetic field phase, behave as further, distinct phases.Comment: 19 pages, typos corrected; to appear in Nucl. Phys.

Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields

Using the Pauli-Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac's vacuum, in the presence of small external electromagnetic sources. The vacuum is not an empty space, but rather a quantum fluctuating medium which behaves as a nonlinear polarizable material. Its behavior is described by a Dirac equation involving infinitely many particles. The quantum corrections to the usual Maxwell equations are nonlinear and nonlocal. Even if photons are described by a purely classical electromagnetic field, the resulting vacuum polarization coincides to first order with that of full Quantum Electrodynamics.Comment: Final version to appear in Arch. Rat. Mech. Analysi

The non-linear Schr\"odinger equation and the conformal properties of non-relativistic space-time

The cubic non-linear Schr\"odinger equation where the coefficient of the nonlinear term is a function $F(t,x)$ only passes the Painlev\'e test of Weiss, Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$ are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to the conformal properties of non-relativistic space-time. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background.Comment: Thoroughly revised version, in the light of new interest in non-relativistic conformal tranformation, with a new reference list. 8 pages, LaTex, no figures. To be published in Int. J. Theor. Phy

Parity Invariance and Effective Light-Front Hamiltonians

In the light-front form of field theory, boost invariance is a manifest symmetry. On the downside, parity and rotational invariance are not manifest, leaving the possibility that approximations or incorrect renormalization might lead to violations of these symmetries for physical observables. In this paper, it is discussed how one can turn this deficiency into an advantage and utilize parity violations (or the absence thereof) in practice for constraining effective light-front Hamiltonians. More precisely, we will identify observables that are both sensitive to parity violations and easily calculable numerically in a non-perturbative framework and we will use these observables to constrain the finite part of non-covariant counter-terms in effective light-front Hamiltonians.Comment: REVTEX, 9 page

Application of Pauli-Villars regularization and discretized light-cone quantization to a single-fermion truncation of Yukawa theory

We apply Pauli-Villars regularization and discretized light-cone quantization to the nonperturbative solution of (3+1)-dimensional Yukawa theory in a single-fermion truncation. Three heavy scalars, including two with negative norm, are used to regulate the theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of a new, indefinite-metric Lanczos algorithm. Various observables are extracted from the wave functions, including average multiplicities and average momenta of constituents, structure functions, and a form factor slope.Comment: 21 pages, 7 figures, RevTeX; published version: more extensive data in the tables of v

Gauge-invariant charged, monopole and dyon fields in gauge theories

We propose explicit recipes to construct the euclidean Green functions of gauge-invariant charged, monopole and dyon fields in four-dimensional gauge theories whose phase diagram contains phases with deconfined electric and/or magnetic charges. In theories with only either abelian electric or magnetic charges, our construction is an euclidean version of Dirac's original proposal, the magnetic dual of his proposal, respectively. Rigorous mathematical control is achieved for a class of abelian lattice theories. In theories where electric and magnetic charges coexist, our construction of Green functions of electrically or magnetically charged fields involves taking an average over Mandelstam strings or the dual magnetic flux tubes, in accordance with Dirac's flux quantization condition. We apply our construction to 't Hooft-Polyakov monopoles and Julia-Zee dyons. Connections between our construction and the semiclassical approach are discussed

Exactly solvable model of superstring in Ramond-Ramond plane wave background

We describe in detail the solution of type IIB superstring theory in the maximally supersymmetric plane-wave background with constant null Ramond-Ramond 5-form field strength. The corresponding light-cone Green-Schwarz action found in hep-th/0112044 is quadratic in both bosonic and fermionic coordinates. We find the spectrum of the light-cone Hamiltonian and the string representation of the supersymmetry algebra. The superstring Hamiltonian has a ``harmonic-oscillator'' form in both the string-oscillator and the zero-mode parts and thus has discrete spectrum in all 8 transverse directions. We analyze the structure of the zero-mode sector of the theory, establishing the precise correspondence between the lowest-lying ``massless'' string states and the type IIB supergravity fluctuation modes in the plane-wave background. The zero-mode spectrum has certain similarity to the supergravity spectrum in AdS_5 x S^5 of which the plane-wave background is a special limit. We also compare the plane-wave string spectrum with expected form of the light-cone gauge spectrum of superstring in AdS_5 x S^5.Comment: 33 pages, latex. v4: minor sign corrections in (1.5) and (3.62), to appear in PR