The Method of Geodesic Expansion

Abstract

The quantization of the bosonic string in a general curved space-time has been the subject of intensive research for some time [1, 2, 3, 4]. Whereas the treatment by de Vega [1] relies on the canonical quantization, only few attempts of a path integral quantization have been made. Those attempts [3, 4] involved the semi-classical approximation, but despite their conceptual simplicity no attempt was made to reproduce the critical dimension in flat space-time, which would have been an indication for the validity of the results. In fact, the path integral measure was treated naively in [3], while a mistake in [4] will become clear in this letter. The aim of this letter is to provide the very first step of the semiclassical treatment of the path integral for the bosonic string in curved space-time, namely a covariant and unambiguous expansion scheme as well as the appropriate path integral measure. The proposed method is applicable to the semiclassical treatment of path integrals in any curved functional space. Hence, it shall be formulated in general terms. ∗e-mail: wmueck@sfu.ca

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