A Stochastic approach to the Virasoro anomaly in quantization of strings in at space

The projective action of the Lie algebra of the diieomorphisms of the circle on the algebraic Fock space CZ 1 ; Z 2 ; : : :] of holomorphic polynomials in innnitely many variables leads to the well-known Virasoro anomaly of string theory. In this article we rst derive the formulas for the Virasoro generators acting on CZ 1 ; Z 2 ; : : :] by means of the reprojection procedure of geometric quantization for non-quantizable functions. Using a generalised stochastic process as the \symplectic trajectory", we obtain the anomaly then by proving an integration-by-parts formula on Wiener space as a commutator anomaly of operators on a Hilbert space of holomorphic L 2-functions on , that naturally completes the algebraic Fock space. Introduction Section 1: Weighted Bargmann-Fock quantization in nite dimensions Section 2: Naive quantization of strings in at space Section 3: The half-derivative of the Brownian bridge as the \symplectic trajectory" Section 4: The Virasoro anomaly in the stochastic approach References