arXiv subjects

Hans-Juergen Matschull

Publications and source records attributed to Hans-Juergen Matschull.

11 recordsLinked to original sources

arXiv2001

The 2+1 Kepler Problem and Its Quantization

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass frame. When the system is quantized, we find some possibly general effects of quantum gravity, such as a minimal distances and a foaminess of the spacetime at the order of the Planck length. We also obtain a quantization of geometry, which restricts the possible asymptotic geometries of the universe.

gr-qc↗

arXiv2001

The Phase Space Structure of Multi Particle Models in 2+1 Gravity

What can we learn about quantum gravity from a simple toy model, without actually quantizing it? The toy model consists of a finite number of point particles, coupled to three dimensional Einstein gravity. It has finitely many physical degrees of freedom. These are basically the relative positions of the particles in spacetime and the conjugate momenta. The resulting reduced phase space is derived from Einstein gravity as a topological field theory. The crucial point is thereby that we do not make any a priori assumptions about this phase space, except that the dynamics of the gravitational field is defined by the Einstein Hilbert action. This already leads to some interesting features of the reduced phase space, such as a non-commutative structure of spacetime when the model is quantized.

gr-qc↗

arXiv2000

(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame

We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but possibly spinning particle. The reduced phase space Γ_{red} has dimension four and topology R^3 x S^1. Γ_{red} is analogous to the phase space of a Newtonian two-body system in the centre-of-mass frame, and we find on Γ_{red} a canonical chart that makes this analogue explicit and reduces to the Newtonian chart in the appropriate limit. Prospects for quantization are commented on.

gr-qc↗

arXiv1999

On the relation between 2+1 Einstein gravity and Chern Simons theory

A simple example is given to show that the gauge equivalence classes of physical states in Chern Simons theory are not in one-to-one correspondence with those of Einstein gravity in three spacetime dimensions. The two theories are therefore not equivalent. It is shown that including singular metrics into general relativity has more, and in fact a quite counter-intuitive, impact on the theory than one naively expects.

gr-qc↗

arXiv1998

Black Hole Creation in 2+1 Dimensions

When two point particles, coupled to three dimensional gravity with a negative cosmological constant, approach each other with a sufficiently large center of mass energy, then a BTZ black hole is created. An explicit solution to the Einstein equations is presented, describing the collapse of two massless particles into a non-rotating black hole. Some general arguments imply that massive particles can be used as well, and the creation of a rotating black hole is also possible.

gr-qc↗

arXiv1998

Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity

We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive at a reduced action for a gravitating particle in 2+1 dimensions, which is invariant under Lorentz transformations and a group of generalized translations. The momentum space of the particle turns out to be the group manifold SL(2). Its position coordinates have non-vanishing Poisson brackets, resulting in a non-commutative quantum spacetime. We use the representation theory of SL(2) to investigate its structure. We find a discretization of time, and some semi-discrete structure of space. An uncertainty relation forbids a fully localized particle. The quantum dynamics is described by a discretized Klein Gordon equation.

gr-qc↗

arXiv1996

Dirac's Canonical Quantization Programme

This is a collection of lectures given at the University of Heidelberg, especially but not exclusively for people who want to learn something about the canonical approach to quantum gravity, which is however not included in these lectures. They are about Dirac's general method to construct a quantum theory out of a classical theory, which has to be defined in terms of a Lagrangian. The classical Hamiltonian formalism is reviewed, with emphasis on the relation between constraints and gauge symmetries, and quantization is carried out without any kind of gauge fixing. The method is applied to three examples: the free electro-magnetic field, the relativistic point particle, and the very first steps of string theory are carried out.

quant-ph↗

arXiv1995

Causal structure and diffeomorphismsm in Ashtekar's gravity

A manifestly diffeomorphism invariant extension of Einstein gravity is constructed, which includes singular metrics, and whose ADM formulation is Ashtekar's gravity. The latter is shown to be locally equivalent to the covariant theory. It turns out that exactly those kinds of degenerate four dimensional metrics are allowed which do not destroy the causal structure of spacetime. It is also shown that Ashtekar's gravity possesses an extension that provides a local SO(3,C) invariance, without complexifying or changing the signature of the metric.

gr-qc↗

arXiv1995

Three Dimensional Canonical Quantum Gravity

General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general relativity, which will later be identified with quantum observers. A precise definition of gauge symmetries and a classification of inequivalent solutions of Einstein's equations in dreibein formalism is given as well. In the quantum part the construction of the physical Hilbert space is carried out explicitly for a torus and cylinder type space manifold, which has not been done so far. Some conceptual problems of quantum gravity are discussed from the point of view of an observer sitting inside the universe.

gr-qc↗

arXiv1994

New representation and a vacuum state for canonical quantum gravity

A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal state functional can be given, which has some typical features of a vacuum state in quantum field theory. It can be canonically transformed into the metric representation. Transforming the constraints too, one recovers the Wheeler~DeWitt equation up to an anomalous term. A modified Dirac quantization is proposed to handle possible anomalies in the constraint algebra.

gr-qc↗

arXiv1994

About Loop States in Supergravity

The Wilson loop functionals in terms of Ashtekar's variables were the first (formal) solutions to the quantized hamiltonian constraint of canonical gravity. Here it is shown that the same functionals also solve the supergravity constraints and some evidence is presented that they are artificially generated by multiplying the constraints by the metric determinant, which has become a widely accepted procedure. Using the same method in 2+1 dimensional gravity and supergravity leads to wrong results, e.g.~2+1 gravity is no longer a purely topological theory. As another feature of the densitized constraints it turns out that the classical theory desribed by them is not invariant under space time diffeomorphisms.

gr-qc↗