Canonical quantization approach to 2d gravity coupled to c<1 matter

Details Canonical quantization approach to 2d gravity coupled to c<1 matter Canonical quantization approach to 2d gravity coupled to c<1 matter

1993-02-15

arxiv.org/abs/hep-th/9302067v1

Int.J.Mod.Phys.A9:4195-4210,1994

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, Imperial-TP/92-93/15, LaTex file

Scientific paper

10.1142/S0217751X94001710

We show that all important features of 2d gravity coupled to $c<1$ matter can be easily understood from the canonical quantization approach a la Dirac. Furthermore, we construct a canonical transformation which maps the theory into a free-field form, i.e. the constraints become free-field Virasoro generators with background charges. This implies the gauge independence of the David-Distler-Kawai results, and also proves the free-field assumption which was used for obtaining the spectrum of the theory in the conformal gauge. A discussion of the unitarity of the physical spectrum is presented and we point out that the scalar products of the discrete states are not well defined in the standard Fock space framework.

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