Canonical Quantization of 2d Gravity Coupled to c<1 Matter

A. Mikovic

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arXiv · hep-th/9202055

Canonical Quantization of 2d Gravity Coupled to c<1 Matter

A. Mikovic

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Abstract

We study 2d gravity coupled to $c,1$ matter through canonical quantization of a free scalar field, with background charge, coupled to gravity. Various features of the theory can be more easily understood in the canonical approach, like gauge indipendence of the path-integral results and the absence of the local physical degrees of freedom. By performing a non-canonical transformation of the phase space variables, we show that the theory takes a free-field form, i.e. the constraints become the free-field Virasoro constraints. This implies that the David-Distler-Kawai results can be derived in the gauge indipendent way, 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 physical spectrum of the theory is presented, with an analysis of the unitarity of the discrete momentum states.

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A. Mikovic. 1992-02-26. Canonical Quantization of 2d Gravity Coupled to c<1 Matter. https://arxiv.org/abs/hep-th/9202055

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