71 research outputs found
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 only passes the Painlev\'e test of Weiss,
Tabor, and Carnevale only for , where and 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
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