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 $W_{\infty }$ 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

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

Quantum Group Covariance and the Braided Structure of Deformed Oscillators

The connection between braided Hopf algebra structure and the quantum group covariance of deformed oscillators is constructed explicitly. In this context we provide deformations of the Hopf algebra of functions on SU(1,1). Quantum subgroups and their representations are also discussed.Comment: 12 pages, to be published in JM

Exact computation of one-loop correction to energy of spinning folded string in AdS_5 x S^5

We consider the 1-loop correction to the energy of folded spinning string solution in the AdS_3 part of AdS_5 x S^5. The classical string solution is expressed in terms of elliptic functions so an explicit computation of the corresponding fluctuation determinants for generic values of the spin appears to be a non-trivial problem. We show how it can be solved exactly by using the static gauge expression for the string partition function (which we demonstrate to be equivalent to the conformal gauge one) and observing that all the corresponding second order fluctuation operators can be put into the standard (single-gap) Lam\'e form. We systematically derive the small spin and large spin expansions of the resulting expression for the string energy and comment on some of their applications.Comment: 52 pp, 12 figures; v3: footnote 9 adde

Braided Oscillators

The braided Hopf algebra structure of the generalized oscillator is investigated. Using the solutions two types of braided Fibonacci oscillators are introduced. This leads to two types of braided Biedenharn-Macfarlane oscillators.Comment: 12 pages, latex, some references added, published versio

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

Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.Comment: 4 pages, Plain Tex, 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.