4,990 research outputs found
Practically linear analogs of the Born-Infeld and other nonlinear theories
I discuss theories that describe fully nonlinear physics, while being
practically linear (PL), in that they require solving only linear differential
equations. These theories may be interesting in themselves as manageable
nonlinear theories. But, they can also be chosen to emulate genuinely nonlinear
theories of special interest, for which they can serve as approximations. The
idea can be applied to a large class of nonlinear theories, exemplified here
with a PL analogs of scalar theories, and of Born-Infeld (BI) electrodynamics.
The general class of such PL theories of electromagnetism are governed by a
Lagrangian L=-(1/2)F_mnQ^mn+ S(Q_mn), where the electromagnetic field couples
to currents in the standard way, while Qmn is an auxiliary field, derived from
a vector potential that does not couple directly to currents. By picking a
special form of S(Q_mn), we can make such a theory similar in some regards to a
given fully nonlinear theory, governed by the Lagrangian -U(F_mn). A
particularly felicitous choice is to take S as the Legendre transform of U. For
the BI theory, this Legendre transform has the same form as the BI Lagrangian
itself. Various matter-of-principle questions remain to be answered regarding
such theories. As a specific example, I discuss BI electrostatics in more
detail. As an aside, for BI, I derive an exact expression for the
short-distance force between two arbitrary point charges of the same sign, in
any dimension.Comment: 20 pages, Version published in Phys. Rev.
"Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions
We develop integration-by-parts rules for Feynman diagrams involving massive
scalar propagators in a constant background electromagnetic field, and use
these to show that there is a simple diagrammatic interpretation of mass
renormalization in the two-loop scalar QED Heisenberg-Euler effective action
for a general constant background field. This explains why the square of a
one-loop term appears in the renormalized two-loop Heisenberg-Euler effective
action. No integrals need be evaluated, and the explicit form of the background
field propagators is not needed. This dramatically simplifies the computation
of the renormalized two-loop effective action for scalar QED, and generalizes a
previous result obtained for self-dual background fields.Comment: 13 pages; uses axodraw.st
Magnetic-field Induced Screening Effect and Collective Excitations
We explicitly construct the fermion propagator in a magnetic field background
B to take the lowest Landau-level approximation. We analyze the energy and
momentum dependence in the polarization tensor and discuss the collective
excitations. We find there appear two branches of collective modes in one of
two transverse gauge particles; one represents a massive and attenuated gauge
particle and the other behaves similar to the zero sound at finite density.Comment: 5 pages, 3 figures; references on the zero sound added and typos
correcte
Fermion Determinants
The current status of bounds on and limits of fermion determinants in two,
three and four dimensions in QED and QCD is reviewed. A new lower bound on the
two-dimensional QED determinant is derived. An outline of the demonstration of
the continuity of this determinant at zero mass when the background magnetic
field flux is zero is also given.Comment: 10 page
On the QED Effective Action in Time Dependent Electric Backgrounds
We apply the resolvent technique to the computation of the QED effective
action in time dependent electric field backgrounds. The effective action has
both real and imaginary parts, and the imaginary part is related to the pair
production probability in such a background. The resolvent technique has been
applied previously to spatially inhomogeneous magnetic backgrounds, for which
the effective action is real. We explain how dispersion relations connect these
two cases, the magnetic case which is essentially perturbative in nature, and
the electric case where the imaginary part is nonperturbative. Finally, we use
a uniform semiclassical approximation to find an expression for very general
time dependence for the background field. This expression is remarkably similar
in form to Schwinger's classic result for the constant electric background.Comment: 27 pages, no figures; reference adde
Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls
We extend our previous results of simplified expressions for functional
determinants for radial Schr\"odinger operators to the computation of vacuum
energy, or mass corrections, for static but spatially radial backgrounds, and
for domain wall configurations. Our method is based on the zeta function
approach to the Gel'fand-Yaglom theorem, suitably extended to higher
dimensional systems on separable manifolds. We find new expressions that are
easy to implement numerically, for both zero and nonzero temperature.Comment: 30 page
The Landau problem and noncommutative quantum mechanics
The conditions under which noncommutative quantum mechanics and the Landau
problem are equivalent theories is explored. If the potential in noncommutative
quantum mechanics is chosen as with defined in the
text, then for the value (that
measures the noncommutative effects of the space), the Landau problem and
noncommutative quantum mechanics are equivalent theories in the lowest Landau
level. For other systems one can find differents values for
and, therefore, the possible bounds for should be searched in
a physical independent scenario. This last fact could explain the differents
bounds for found in the literature.Comment: This a rewritten and corrected version of our previous preprint
hep-th/010517
Photoproduction in semiconductors by onset of magnetic field
The energy bands of a semiconductor are lowered by an external magnetic
field. When a field is switched on, the straight-line trajectories near the top
of the occupied valence band are curved into Landau orbits and Bremsstrahlung
is emitted until the electrons have settled in their final Fermi distribution.
We calculate the radiated energy, which should be experimentally detectable,
and suggest that a semiconductor can be cooled by an oscillating magnetic
field
Consistency restrictions on maximal electric field strength in QFT
QFT with an external background can be considered as a consistent model only
if backreaction is relatively small with respect to the background. To find the
corresponding consistency restrictions on an external electric field and its
duration in QED and QCD, we analyze the mean energy density of quantized fields
for an arbitrary constant electric field E, acting during a large but finite
time T. Using the corresponding asymptotics with respect to the dimensionless
parameter , one can see that the leading contributions to the energy are
due to the creation of paticles by the electric field. Assuming that these
contributions are small in comparison with the energy density of the electric
background, we establish the above-mentioned restrictions, which determine, in
fact, the time scales from above of depletion of an electric field due to the
backreactionComment: 7 pages; version accepted for publication in Phys. Rev. Lett.; added
one ref. and some comment
The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
Particle production due to external fields (electric, chromo-electric or
gravitational) requires evolving an initial state through an interaction with a
time-dependent background, with the rate being computed from a Bogoliubov
transformation between the in and out vacua. When the background fields have
temporal profiles with sub-structure, a semiclassical analysis of this problem
confronts the full subtlety of the Stokes phenomenon: WKB solutions are only
local, while the production rate requires global information. Incorporating the
Stokes phenomenon, we give a simple quantitative explanation of the recently
computed [Phys. Rev. Lett. 102, 150404 (2009)] oscillatory momentum spectrum of
e+e- pairs produced from vacuum subjected to a time-dependent electric field
with sub-cycle laser pulse structure. This approach also explains naturally why
for spinor and scalar QED these oscillations are out of phase.Comment: 5 pages, 4 figs.; v2 sign typo corrected, version to appear in PR
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