2D Quantum Gravity in the Proper-Time Gauge

Details 2D Quantum Gravity in the Proper-Time Gauge 2D Quantum Gravity in the Proper-Time Gauge

1993-12-20

arxiv.org/abs/hep-th/9312158v1

Phys.Lett. B325 (1994) 347-353

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, latex

Scientific paper

10.1016/0370-2693(94)90023-X

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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