Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1994-06-16
Lect.Notes Phys. 436 (1994) 98-122
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
26, pages, TUW-94-2
Scientific paper
10.1007/3-540-58453-6_6
Pure gravity and gauge theories in two dimensions are shown to be special cases of a much more general class of field theories each of which is characterized by a Poisson structure on a finite dimensional target space. A general scheme for the quantization of these theories is formulated. Explicit examples are studied in some detail. In particular gravity and gauge theories with equivalent actions are compared. Big gauge transformations as well as the condition of metric nondegeneracy in gravity turn out to cause significant differences in the structure of the corresponding reduced phase spaces and the quantum spectra of Dirac observables. For $R^2$ gravity coupled to SU(2) Yang Mills the question of quantum dynamics (`problem of time') is addressed. [This article is a contribution to the proceedings (to appear in LNP) of the 3rd Baltic RIM Student Seminar (1993). Importance is attached to concrete examples. A more abstract presentation of the ideas underlying this article (including new developments) is found in hep-th/9405110.]
Schaller Peter
Strobl Thomas
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