8,105 research outputs found
The Euler-Heisenberg Lagrangian beyond one loop
We review what is presently known about higher loop corrections to the
Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those
corrections as a tool for the study of the properties of the QED perturbation
series is outlined. As a further step in a long-term effort to prove or
disprove the convergence of the N photon amplitudes in the quenched
approximation, we present a parameter integral representation of the three-loop
Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline
formalism.Comment: 11 pages, 2 figures, talk given by Christian Schubert at QFEXT11,
Benasque, Spain, Sept. 18-24, 2011, to appear in the conference proceeding
Symmetry Aspects and Finite-Size Scaling of Quantum Hall Fluids
The exactness and universality observed in the quantum Hall effect suggests
the existence of a symmetry principle underlying Laughlin's theory. We review
the role played by the infinite and conformal algebras as
dynamical symmetries of incompressible quantum fluids and show how they predict
universal finite-size effects in the excitation spectrum.Comment: 15 pages, CERN-TH-6784/93, LateX fil
Exotic galilean symmetry and the Hall effect
The ``Laughlin'' picture of the Fractional Quantum Hall effect can be derived
using the ``exotic'' model based on the two-fold centrally-extended planar
Galilei group. When coupled to a planar magnetic field of critical strength
determined by the extension parameters, the system becomes singular, and
``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne,
Jackiw, and Trugenberger. The reduced system moves according to the Hall law.Comment: Talk given by P. A. Horvathy at the Joint APCTP- Nankai Symposium.
Tianjin (China), Oct.2001. To appear in the Proceedings, to be published by
Int. Journ. Mod. Phys. B. 7 pages, LaTex, IJMPB format. no figure
Exotic plasma as classical Hall Liquid
A non-relativistic plasma model endowed with an ``exotic'' structure
associated with the two-parameter central extension of the planar Galilei group
is constructed. Introducing a Chern-Simons statistical gauge field provides us
with a self-consistent system; when the magnetic field takes a critical value
determined by the extension parameters, the fluid becomes incompressible and
moves collectively, according to the Hall law.Comment: 11 pages, LaTex, no figures. Revised version: Some details better
explained. To appear in Int. Journ. Mod. Phys.
Geometrical foundations of fractional supersymmetry
A deformed -calculus is developed on the basis of an algebraic structure
involving graded brackets. A number operator and left and right shift operators
are constructed for this algebra, and the whole structure is related to the
algebra of a -deformed boson. The limit of this algebra when is a -th
root of unity is also studied in detail. By means of a chain rule expansion,
the left and right derivatives are identified with the charge and covariant
derivative encountered in ordinary/fractional supersymmetry and this leads
to new results for these operators. A generalized Berezin integral and
fractional superspace measure arise as a natural part of our formalism. When
is a root of unity the algebra is found to have a non-trivial Hopf
structure, extending that associated with the anyonic line. One-dimensional
ordinary/fractional superspace is identified with the braided line when is
a root of unity, so that one-dimensional ordinary/fractional supersymmetry can
be viewed as invariance under translation along this line. In our construction
of fractional supersymmetry the -deformed bosons play a role exactly
analogous to that of the fermions in the familiar supersymmetric case.Comment: 42 pages, LaTeX. To appear in Int. J. Mod. Phys.
Mass Spectra of N=2 Supersymmetric SU(n) Chern-Simons-Higgs Theories
An algebraic method is used to work out the mass spectra and symmetry
breaking patterns of general vacuum states in N=2 supersymmetric SU(n)
Chern-Simons-Higgs systems with the matter fields being in the adjoint
representation. The approach provides with us a natural basis for fields, which
will be useful for further studies in the self-dual solutions and quantum
corrections. As the vacuum states satisfy the SU(2) algebra, it is not
surprising to find that their spectra are closely related to that of angular
momentum addition in quantum mechanics. The analysis can be easily generalized
to other classical Lie groups.Comment: 17 pages, use revte
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
A Gauge-Gravity Relation in the One-loop Effective Action
We identify an unusual new gauge-gravity relation: the one-loop effective
action for a massive spinor in 2n dimensional AdS space is expressed in terms
of precisely the same function [a certain multiple gamma function] as the
one-loop effective action for a massive charged scalar in 4n dimensions in a
maximally symmetric background electromagnetic field [one for which the
eigenvalues of F_{\mu\nu} are maximally degenerate, corresponding in 4
dimensions to a self-dual field, equivalently to a field of definite helicity],
subject to the identification F^2 \Lambda, where \Lambda is the
gravitational curvature. Since these effective actions generate the low energy
limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a
nontrivial gauge-gravity relation at the non-perturbative level and at the
amplitude level.Comment: 6 page
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