A local diagnostic program for unitary evolution in general space-times

Abstract

We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of observables and solely employs geometric concepts in the functional representation of quantum field theory. In this representation, it is possible to construct infinitely many self-adjoint extensions of the canonical momentum field at the kinematic level, and by the usual functional calculus arguments this holds for the Hamiltonian, as well. However, these self-adjoint domains have only the trivial wave functional in common with the solution space of the functional Schrödinger equation. This is related to the existence of boundaries in configuration field space which can be penetrated by the probability flux, causing probability to leak into regions in configuration field space that require a more fundamental description. As a consequence the evolution admits no unitary representation. Instead, in the absence of ghosts, the evolution is represented by contractive semi-groups in the semiclassical approximation. This allows to quantify the unitarity loss and, in turn, to assess the quality of the semi-classical approximation. We perform numerical experiments based on our formal investigations to determine regions in cosmological spacetimes where the semiclassical approximation breaks down for free quantum fields.

20 pages, 7 figures

References in corpus (18)

• On Geometric Entropy
• Power-counting and the Validity of the Classical Approximation During Inflation
• Multiscale Gaussian Random Fields for Cosmological Simulations
• Semiclassical Gravity Theory and Quantum Fluctuations
• Non-Equilibrium Evolution of Scalar Fields in FRW Cosmologies I
• Dynamics of entanglement in expanding quantum fields
• Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space
• Quantum Fields at Any Time
• The Schrodinger Wave Functional and Vacuum States in Curved Spacetime
• Classical versus quantum completeness
• On the Schroedinger Representation for a Scalar Field on Curved Spacetime
• Unitary and non-unitary evolution in quantum cosmology
• Quantum Spacetime Instability and Breakdown of Semiclassical Gravity
• A Quantum Complete Prelude to Inflation
• Non-Gaussian ground-state deformations near a black-hole singularity
• Hybrid Geometrodynamics: A Hamiltonian description of classical gravity coupled to quantum matter
• Geometric flavours of Quantum Field theory on a Cauchy hypersurface. Part II: Methods of quantization and evolution
• Geometric flavours of Quantum Field theory on a Cauchy hypersurface. Part I: Gaussian analysis and other Mathematical aspects