Quantization of the Reduced Phase Space of Two-Dimensional Dilaton Gravity

Abstract

We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient (static) gauge we reduce the theory to coupled \ode s and we are able to derive for some potentials of interest closed-form solutions. We use an effective (particle) Lagrangian for the reduced field equations in order to quantize the system in a finite-dimensional setting leading to an exact partial differential Wheeler-DeWitt equation instead of a functional one. A WKB approximation for some quantum states is computed and compared with the classical Hamilton-Jacobi theory. The effect of minimally coupled matter is examined.

19 pages, LaTeX

References in corpus (7)

• Exact Dirac Quantization of All 2-D Dilaton Gravity Theories
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• The Black Holes of a General Two-Dimensional Dilaton Gravity Theory
• Involution and Constrained Dynamics I: The Dirac Approach
• Black holes in generalized dilaton gravity in two dimensions
• On the Relation between Classical and Quantum Cosmology in a 2-Dimensional Dilaton-Gravity Model
• On The Reduced Canonical Quantization Of The Induced 2D-Gravity

Cited by in corpus (6)

• Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach
• Exact Path Integral Quantization of Generic 2-D Dilaton Gravity
• Integrating Geometry in General 2D Dilaton Gravity with Matter
• The virtual black hole in 2d quantum gravity
• Nonperturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter
• Absolute conservation law for black holes