Wheeler-DeWitt Equation in Two-dimensional Quantum Gravity with $c=1$ Conformal Matter Field

Details Wheeler-DeWitt Equation in Two-dimensional Quantum Gravity with $c=1$ Conformal Matter Field Wheeler-DeWitt Equation in Two-dimensional Quantum Gravity with $c=1$ Conformal Matter Field

1993-12-24

arxiv.org/abs/hep-th/9312191v2

Phys.Rev. D50 (1994) 2609-2614

Physics

High Energy Physics

High Energy Physics - Theory

14p, LaTex

Scientific paper

10.1103/PhysRevD.50.2609

In the context of two-dimensional quantum cosmology, we consider the path-integral of a string on annulus which contains the Liouville field and conformal matter fields. We show that, in the transition amplitude of the string universe, the non-zero modes of the fields are all cancelled out only when we take the $c=1$ conformal matter field and impose the Neumann boundary condition on the system. The transition amplitude obtained obeys the minisuperspace Wheeler-DeWitt equation. In our treatment, the modular parameter on annulus plays the role of time variable to integrate out.

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