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arXiv · hep-th/9904057

Perturbative or Path-Integral Approach versus Operator-Formalism Approach

Mitsuo Abe·Noboru Nakanishi
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Abstract

In the conformal-gauge two-dimensional quantum gravity, the solution obtained by the perturbative or path-integral approach is compared with the one obtained by the operator-formalism approach. Treatments of the anomaly problem in both approaches are different. This difference is found to be essentially caused by the fact that the perturbative or path-integral approach is based on the T*-product (covariantized T-product), which generally violates field equations. Indeed, this fact induces some extra one-loop Feynman diagrams, which would not exist unless a nonzero contribution arose from a zero field. Some demerits of the path-integral approach are explicitly demonstrated.

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Mitsuo Abe, Noboru Nakanishi. 1999-04-08. Perturbative or Path-Integral Approach versus Operator-Formalism Approach. https://doi.org/10.1143/ptp.102.1187

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