General Covariance and Free Fields in Two Dimensions
نویسندگان
چکیده
We investigate the canonical equivalence of a matter-coupled 2D dilaton gravity theory defined by the action functional S = d 2 x √ −g (Rφ + V (φ) − 1 2 H (φ) (∇f) 2 , and a free field theory. When the scalar field f is minimally coupled to the metric field (H(φ) = 1) the theory is equivalent, up to a boundary contribution, to a theory of three free scalar fields with indefinite kinetic terms, irrespective of the particular form of the potential V (φ). If the potential is an exponential function of the dilaton one recovers a generalized form of the classical canonical transformation of Liouville theory. When f is a dilaton coupled scalar (H(φ) = φ) and the potential is an arbitrary power of the dilaton the theory is also canonically equivalent to a theory of three free fields with a Minkowskian target space. In the simplest case (V (φ) = 0) we provide an explicit free field realization of the Einstein-Rosen midisu-perspace. The Virasoro anomaly and the consistence of the Dirac operator quantization play a central role in our approach.
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