W. Kummer

Nonconservation of total lepton number with scalar bosons

Abstract The role of scalar bosons is studied in connection with a violation of the number of fermions + antifermions. Some simple estimates of the transitions μ → e λ and μ → 3e are based upon a minimal extension of the “standard” gauge model of weak and electromagnetic interactions.

Exact path integral quantization of generic 2D dilaton gravity

Abstract Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall-off conditions for all fields. We demonstrate that in the absence of “matter” fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one. This resolves the apparent contradiction between the well-established results of Dirac quantization and perturbative (path-integral) approaches which seemed to yield non-trivial quantum corrections. For a particular case, the Jackiw-Teitelboim model, our result is even extended to the situation when a matter field is present.

The classical solutions of the dimensionally reduced gravitational Chern–Simons theory

The Kaluza-Klein reduction of the 3d gravitational Chern-Simons term to a 2d theory is equivalent to a Poisson-sigma model with fourdimensional target space and degenerate Poisson tensor of rank 2. Thus two constants of motion (Casimir functions) exist, namely charge and energy. The application of well-known methods developed in the framework of first order gravity allows to construct all classical solutions straightforwardly and to discuss their global structure. For a certain fine tuning of the values of the constants of motion the solutions of hep-th/0305117 are reproduced. Possible generalizations are pointed out.

On the completeness of the black hole singularity in 2D dilaton theories

Abstract The black hole of the widely used ordinary 2D-dilaton model (DBH) deviates from the Schwarzschild black hole (SBH) of General Relativity in one important feature: Whereas non-null extremals or geodesics show the expected incompleteness this turns out not to be the case for the null extremals . After a simple analysis in Kruskal coordinates for singularities with power behavior of this - apparently up to now overlooked - property we discuss the global structure of a large family of generalized dilaton theories which does not only contain the DBH and SBH but also other proposed dilaton theories as special cases. For large ranges of the parameters such theories are found to be free from this defect and exhibit global SBH behavior.

Integrating Geometry in General 2D Dilaton Gravity with Matter

Abstract General 2d dilaton theories, containing spherically symmetric gravity and hence the Schwarzschild black hole as a special case, are quantized by an exact path integral of their geometric (Cartan) variables. Matter, represented by minimally coupled massless scalar fields is treated in terms of a systematic perturbation theory. The crucial prerequisite for our approach is the use of a temporal gauge for the spin connection and for light-cone components of the zweibeins which amounts to an Eddington-Finkelstein gauge for the metric. We derive the generating functional in its most general form which allows a perturbation theory in the scalar fields. The relation of the zero order functional to the classical solution is established. As an example we derive the ffective (gravitationally) induced 4-vertex for scalar fields.

Geometric Interpretation and Classification of Global Solutions in Generalized Dilaton Gravity

Two dimensional gravity with torsion is proved to be equivalent to special types of generalized 2d dilaton gravity. E.g. in one version, the dilaton field is shown to be expressible by the extra scalar curvature, constructed for an independent Lorentz connection corresponding to a nontrivial torsion. Elimination of that dilaton field yields an equivalent torsionless theory, nonpolynomial in curvature. These theories, although locally equivalent exhibit quite different global properties of the general solution. We discuss the example of a (torsionless) dilaton theory equivalent to the R 2 + T 2 –model. Each global solution of this model is shown to split into a set of global solutions of generalized dilaton gravity. In contrast to the theory with torsion the equivalent dilaton one exhibits solutions which are asymptotically flat in special ranges of the parameters. In the simplest case of ordinary dilaton gravity we clarify the well kown problem of removing the Schwarzschild singularity by a field redefinition.

Novel symmetry of non‐Einsteinian gravity in two dimensions

The integrability of R2‐gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space. It may be interpreted as a quadratically deformed iso(2,1)‐algebra with the deformation consisting of the Casimir operators of the undeformed algebra. The locally conserved quantity encountered in the explicit solution is identified as an element of the center of this algebra. Specific contractions of the algebra are related to specific limits of the explicit solutions of this model.

Renormalization of R2 gravity with dynamical torsion in d=2

Expressed in terms of zweibein and spin-connection, non-einsteinian gravity in d = 2 resembles a gauge theory with noncompact group and with nonpolynomial self-interactions. We show that this theory, nevertheless, is renormalizable because an infinite set of counterterms in the effective action may be expressed by one renormalizable quantity. Our analysis is based upon the use of a light-cone gauge where the UV behaviour, but especially also severe IR problems are more amenable to analysis than in a covariant gauge.

The virtual black hole in 2d quantum gravity

Abstract As shown recently (W. Kummer, H. Liebl, D.V. Vassilevich, Nucl. Phys. B 544 (1999) 403) 2d quantum gravity theories — including spherically reduced Einstein-gravity — after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the classical mechanism of black hole formation should be contained in the tree approximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hole mass is identified as a “virtual black hole”. The present discussion is restricted to minimally coupled scalars without and with mass. In the first case the probability amplitude diverges, except the black hole is “plugged” by a suitable boundary condition. For massive scalars a finite S -matrix element is obtained.

Unitary in the ghost-free axial gauge

Abstract It is shown that gauge theories formulated in the ghost-free axial gauge n · A = 0 yield a unitary S -matrix.