Unitarity and ultraviolet regularity in cosmology

Abstract

Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time dependent space-times ---including the simplest cosmological models--- dynamics of quantum fields is not unitary in the standard sense. This issue is first explained with an explicit example and it is then shown that a generalized notion of unitarity does hold. The generalized notion allows one to correctly pass to the Schrödinger picture starting from the Heisenberg picture used in the textbook treatments. Finally, we indicate how these considerations can be extended from simple cosmological models to general globally hyperbolic space-times

30 pages, 0 figures. Version to be published in PRD

References in corpus (10)

• Matter creation in a nonsingular bouncing cosmology
• Preferred instantaneous vacuum for linear scalar fields in cosmological space-times
• Quantum Gowdy $T^3$ model: A uniqueness result
• Uniqueness of the Fock quantization of the Gowdy $T^3$ model
• Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes
• The Creation of Particles in an Expanding Universe
• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• Quantum unitary evolution of linearly polarized S^1\times S^2 and S^3 Gowdy models coupled to massless scalar fields
• Uniqueness of the Fock quantization of scalar fields under mode preserving canonical transformations varying in time
• Unitary evolution of free massless fields in de Sitter space-time

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