Quantum Field Theory in a Topology Changing Universe

Abstract

We propose a method to construct quantum theory of matter fields in a topology changing universe. Analytic continuation of the semiclassical gravity of a Lorentzian geometry leads to a non-unitary Schrödinger equation in a Euclidean region of spacetime, which does not have a direct interpretation of quantum theory of the Minkowski spacetime. In this Euclidean region we quantize the Euclidean geometry, derive the time-dependent Schrödinger equation and find the quantum states using the Liouville-Neumann method. The Wick rotation of these quantum states provides the correct Hilbert space of matter field in the Euclidean region of the Lorentzian geometry. It is found that the direct quantization of a scalar field in the Lorentzian geometry involves an unusual commutation rule in the Euclidean region. Finally we discuss the interpretation of the periodic solution of the semiclassical gravity equation in the Euclidean geometry as a finite temperature solution for the gravity-matter system in the Lorentzian geometry.

14 pages, RevTex, 1 figure, Revised version resubmitted to Class. Quantum Grav

References in corpus (3)

• Open Inflation Without False Vacua
• Open Inflation, the Four Form and the Cosmological Constant
• Comment on `Quantum Creation of an Open Universe', by Andrei Linde

Cited by in corpus (5)

• Geometric Origin of Stokes Phenomenon for de Sitter Radiation
• Black Hole Decay and Quantum Instantons
• Gravitational Collapse and Calogero Model
• An action principle for the quantization of parametric theories and nonlinear quantum cosmology
• Interplay between the small and the large scale structure of spacetime