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

New relations between spinor and scalar one-loop effective Lagrangians in constant background fields

Simple new relations are presented between the one-loop effective Lagrangians of spinor and scalar particles in constant curvature background fields, both electromagentic and gravitational. These relations go beyond the well-known cases for self-dual background fields

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

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.

Analogies between self-duality and stealth matter source

We consider the problem of a self-interacting scalar field nonminimally coupled to the three-dimensional BTZ metric such that its energy-momentum tensor evaluated on the BTZ metric vanishes. We prove that this system is equivalent to a self-dual system composed by a set of two first-order equations. The self-dual point is achieved by fixing one of the coupling constant of the potential in terms of the nonminimal coupling parameter. At the self-dual point and up to some boundary terms, the matter action evaluated on the BTZ metric is bounded below and above. These two bounds are saturated simultaneously yielding to a vanishing action for configurations satisfying the set of self-dual first-order equations.Comment: 6 pages. To be published in Jour. Phys.

Functional Determinants for Radially Separable Partial Differential Operators

Functional determinants of differential operators play a prominent role in many fields of theoretical and mathematical physics, ranging from condensed matter physics, to atomic, molecular and particle physics. They are, however, difficult to compute reliably in non-trivial cases. In one dimensional problems (i.e. functional determinants of ordinary differential operators), a classic result of Gel’fand and Yaglom greatly simplifies the computation of functional determinants. Here I report some recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators), with applications in quantum field theory.

A Note on Schwinger Mechanism and a Nonabelian Instability in a Nonabelian Plasma

We point out that there is a nonabelian instability for a nonabelian plasma which does not allow both for a net nonzero color charge and the existence of field configurations which are coherent over a volume $v$ whose size is determined by the chemical potential. The basic process which leads to this result is the Schwinger decay of chromoelectric fields, for the case where the field arises from commutators of constant potentials, rather than as the curl of spacetime dependent potentials. In terms of the fields, instability is obtained when Tr(DF)^2 > 0.Comment: 14 pages, 6 figure

Some chirality-related properties of the 4-D massive Dirac propagator and determinant in an arbitrary gauge field

For a 4-D massive Dirac field in the background of arbitrary gauge fields, we show that the Dirac propagator and functional determinant are completely determined by knowledge of the corresponding quantities for just one of the chirality sectors of the second-order Dirac operator. This generalizes the related, previously known, statements in (anti-)self-dual background gauge fields. The logarithms of the (renormalized) functional determinants from the two chirality sectors are shown to be different only by a term reflecting the integrated chiral anomaly.Comment: 17 pages, late

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

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