Functional integral of QED in terms of gauge-invariant quantities

We reduce the functional integral of quantum electrodynamics to an integral containing only local gauge invariant quantities. The set of (bosonic) invariants contains bilinear combinations of the spinor field and a real-valued covector field.     

Simplicial gauge theory and quantum gauge theory simulation

We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionally, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of β.     

Generalized coupling constants for broken gauge symmetries in geometrical terms

A geometrical treatment of the gauge coupling constant is proposed in terms of a generalized connection form using fibre-bundle language. This extends the notion of the coupling constant to a notion of a field. The reduction of a curvature form for the generalized connection form is described in the case of a reduction of a structure group G to a subgroup H (broken gauge symmetry), and a coupling constant for the gauge group H is constructed from the corresponding one for the gauge group G.     

Absence of species doubling in finite-element quantum electrodynamics

In this Letter, it will be demonstrated explicitly that the finite-element formulation of quantum electrodynamics is free from fermion doubling. We do this by (1) examining the lattice fermion propagator and using it to compute the one-loop vacuum polarization on the lattice, and (2) by an explict computation of vector and axial-vector current anomalies for an arbitrary rectangular lattice in the Schwinger model. There it is shown that requiring that the vector current be conserved necessitates the use of a square lattice, in which case the axial-vector current is anomalous.     

Self-dual Vortices in a Maxwell–Chern–Simons Model with Non-minimal Coupling

We study self-dual vortex solutions in a Maxwell – Chern – Simons model with anomalous magnetic moment. We establish the existence of multivortex solutions and obtain the quantized energy and the magnetic flux. We also prove the uniqueness of solutions when there is only one vortex point.      

A new limit for the noncommutative space–time parameter

The spectrum of the hydrogen atom in the framework of noncommutative quantum mechanics is studied and the related phenomenology is presented. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in the atom. To the first order in the noncommutative parameter, it is equivalent to an electron in the fields of a Coulomb potential and an electric dipole and this allows us to get a bound for this parameter. In a second step, we compute noncommutative corrections of the energy levels and find that they are at the second order in the parameter of noncommutativity. By comparing our results to those obtained from experimental spectroscopy, we get another limit for this parameter.     

Splitting of Landau levels in the presence of external potentials

We study the quantum mechanical problem of a charged particle moving in a constant magnetic field and an azimuthally symmetric external potential. We show that the lowest Landau level splits in a definite way if the external potential is a monotone function of the radial distance in the plane orthogonal to the magnetic field. For two-dimensional systems, we give sufficient conditions such that all Landau levels are completely ordered. For the lowest Landau level, this result holds for nonhomogeneous magnetic fields as long as they are cylindrically symmetric.Supported by the Federal Ministry of Science and Research, Austria. Part of Project P8916-PHY of the Fonds zur Förderung der wissenschaftliche Forschung in Österreich.     

Lower bounds on width of Stark resonances in one dimension

We prove a lower bound for the width of Stark resonances in one dimension.     

Generalized link-invariants on 3-manifolds ∑h × [0, 1] from Chern-Simons gauge and gravity theories

We show that the recently found generalized Jones and Homfly polynomials for links in _h × [0, 1], where _h is a closed oriented Riemann surface, may be also obtained by the canonical quantization of a Chern-Simons non-Abelian gauge theory on _h × [0, 1]. As a particular case, one may consider the 2+1-dimensional Euclidean quantum gravity with a positive cosmological constant.     

Electromagnetic duality transformations in supersymmetric field theories

We explore the properties of theories which are invariant under electromagnetic duality.N=2 supergravity Yang-Mills systems are discussed in more details. In particular, a symplectic and coordinate covariant framework is established which allows one to discuss classical and quantum duality symmetries (T andS dualities), as they emerge in superstrings in four dimensions withN=2 spacetime supersymmetry.This article is dedicated to the memory of my friend Julian Schwinger     

Mixed quantum mechanical periodic and potential wall problem

We consider the Schrödinger equation with an even-square integrable potential of period one on the negative real axis and a wall potential of heighta > 0 on the positive real axis. The spectrum of this Schrödinger equation is determined and it is proved that bounded solutions never exist if the energyE < a is lying in a gap of the periodic spectrum.     

On kicked quantum systems

The time evolution of a multi-dimensional quantum system which is kicked at random or periodically with a potential is obtained. An interesting aspect of the evolution is that if the operator corresponding to the potential has invariant subspaces (this is characteristic of multi-dimensional problems), the system evolves in these invariant subspaces, i.e., each evolution in the subspaces is independent and there cannot be any mixing between the states of these subspaces.     

Quantum Riemann surfaces III. the exceptional cases

We discuss quantum deformations of Riemann surfaces whose fundamental groups are Abelian (the exceptional Riemann surfaces). We prove uniformization theorems, state deformation estimates, and study the dependence of quantum Riemann surfaces on the deformation parameter.Supported in part by NSF grant DMS-9206936.Supported in part by DOE grant DE-FG02-88ER25065.     

On the relation between a conformal structure in spacetime and nets of local algebras of observables

In this Letter, we study the question of how to reconstruct the conformal structure (causality relation) of spacetime from a net of local algebras of observables on the underlying manifold.Partly supported by DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

About matrix elements of spatial translations in local field theories

Some results of Fredenhagen concerning the asymptotic behavior of matrix elements of translation operators in local quantum field theories are discussed. An alternative derivation and generalizations are presented.     

Modular inclusion,the Hawking temperature,and quantum field theory in curved spacetime

A recent result by Borchers connecting geometric modular action, modular inclusion and spectrum condition, is applied in quantum field theory on spacetimes with a bifurcate Killing horizon (these are generalizations of black-hole spacetimes, comprising the familiar black-hole spacetime models). Within this framework, we give sufficient, model-independent conditions ensuring that the temperature of thermal equilibrium quantum states is the Hawking temperature.     

Operator ideals and the statistical independence in quantum field theory

We consider analytic properties of a class of dynamical systems which are defined by the action of certain homomorphism groups on von Neumann algebras if restricted to subalgebras. In particular, the analyticity of nuclear maps in the nuclear norm is shown. Furthermore, the statistical independence will be derived from nuclearity conditions. These results give new insight in the statistical independence of commuting algebras.This paper is a result of a collaboration with H. J. Borchers.     

Nuclearity,split property,and duality for the Klein-Gordon field in curved spacetime

Nuclearity, split property and duality are established for the nets of von Neumann algebras associated with the representations of distinguished states of the massive Klein-Gordon field propagating in particular classes of curved spacetimes.Supported by the DFG.     

Generalized nuclearity conditions and the split property in quantum field theory

Generalized nuclearity conditions that are applicable in arbitrary superselection sectors of a quantum field theory and to theories with a maximal temperature are discussed. They are shown to imply the (distal) split property and to impose specific restrictions on the spectral properties of modular operators associated with local algebras and vectors of compact energy support.