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arXiv · hep-th/9312158

2D Quantum Gravity in the Proper-Time Gauge

Ryuichi Nakayama
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Abstract

A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ($g_{00}=1$, $g_{01}=g_{10}=0$) in the continuum formulation. The constraint $T_{01}=0$ is solved and used to reduce the problem of field theory to that of quantum mechanics. This reduction can also be proved by using a conformal Ward identity. The amplitude depends on the lengths $l_1, l_2$ of the boundaries, the proper time $T$ and a non-negative integer $m$ associated with winding modes around the boundaries.

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Ryuichi Nakayama. 1993-12-20. 2D Quantum Gravity in the Proper-Time Gauge. https://doi.org/10.1016/0370-2693(94)90023-x

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