2+1 gravity and Doubly Special Relativity

It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of Doubly Special Relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a $DSR$ system answers a number of questions concerning the latter, and resolves the ambiguity of the basis of the algebra of observables. Based on this observation a heuristic argument is made that the algebra of symmetries of ultra high energy particle kinematics in 3+1 dimensions is described by some DSR theory.Comment: 8 pages Latex, no figures, typos correcte

Darboux coordinates for the Hamiltonian of first order Einstein-Cartan gravity

Based on preliminary analysis of the Hamiltonian formulation of the first order Einstein-Cartan action (arXiv:0902.0856 [gr-qc] and arXiv:0907.1553 [gr-qc]) we derive the Darboux coordinates, which are a unique and uniform change of variables preserving equivalence with the original action in all spacetime dimensions higher than two. Considerable simplification of the Hamiltonian formulation using the Darboux coordinates, compared with direct analysis, is explicitly demonstrated. Even an incomplete Hamiltonian analysis in combination with known symmetries of the Einstein-Cartan action and the equivalence of Hamiltonian and Lagrangian formulations allows us to unambiguously conclude that the \textit{unique} \textit{gauge} invariances generated by the first class constraints of the Einstein-Cartan action and the corresponding Hamiltonian are \textit{translation and rotation in the tangent space}. Diffeomorphism invariance, though a manifest invariance of the action, is not generated by the first class constraints of the theory.Comment: 44 pages, references are added, organization of material is slightly modified (additional section is introduced), more details of calculation of the Dirac bracket between translational and rotational constraints are provide

Kanonische Formulierung von Gravitations- und Supergravitations-Theorien

In this thesis some recent results concerning canonical formulation and ansaetze for quantization of general relativity are presented, which are related to Ashtekar's variables. In the first part the new variables are introduced on the Lagrangian level. The program of chanonical quantization is applied to gravity and supergravity and some ansaetze for solutions to the constraints are discussed, with special emphasis on the singular metric problem of the so called loop states. The second part is concerned with three dimensional models. For pure N=2 supergravity the complete physical state space is constructed by using the canonical method. Finally, the canonical structure of matter coupled N=2 supergravity is worked out and its quantization and an ansatz for a solution to the constraints is discussed. (orig.)SIGLEAvailable from TIB Hannover: RA 2999(94-118) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

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 described by them is not invariant under space time diffeomorphisms. (orig.)Available from TIB Hannover: RA 2999(94-037) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Canonical quantum supergravity in three dimensions

We discuss the canonical treatment and quantization of matter coupled supergravity in three dimensions, with special emphasis on N=2 supergravity. We then analyze the quantum constraint algebra; certain operator ordering ambiguities are found to be absent due to local supersymmetry. We show that the supersymmetry constraints can be partially solved by a functional analog of the method of characteristics. We also consider extensions of Wilson loop integrals of the type previously found in ordinary gravity, but now with connections involving the bosonic and fermionic matter fields in addition to the gravitational connection. In a separate section of this paper, the canonical treatment and quantization of non-linear coset space sigma models are discussed in a self contained way. (orig.)Available from TIB Hannover: RA 2999(93-073) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Physical states in d = 3, N = 2 supergravity

To clarify some issues raised by D'Eath's recent proposal for the physical states of N = 1 supergravity in four dimensions, we study pure (topological) N 2 supergravity in three dimensions, which is formally very similar, but much easier to solve. The wave functionals solving the quantum constraints can be understood in terms of arbitrary functions on the space of moduli and supermoduli, which is not Hausdorff. We discuss the implications for the wave functionals and show that these are not amenable to expansions in fermionic coordinates, but can serve as lowest-order solutions to the quantum constraints in an expansion in #Planck constant# in more realistic theories. (orig.)Available from TIB Hannover: RA 2999(93-125) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman