Failure of unitarity for interacting fields on spacetimes with closed timelike curves

Journal Article · Sun Nov 15 04:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.4456· OSTI ID:7003539

Friedman, J L; Papastamatiou, N J; Simon, J Z ^[1]

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1. Department of Physics, University of Wisconsin, Milwaukee, Wisconsin 53201 (United States)

The scattering of free quantum fields is well defined on a class of asymptotically flat spacetimes with closed timelike curves (CTC's), and, at least on these spacetimes, the {ital S} matrix is unitary as well. For interacting fields, however, the preceding paper has obtained a set of unitarity relations that must be satisfied by the Feynman propagator if the scattering is to be unitary to each order in perturbation theory. In a globally hyperbolic spacetime, the causal form of the propagator guarantees that the relations are satisfied, but for spacetimes with CTC's, the form of the propagator is altered, and we show that the unitarity relations are not satisfied for interacting fields. We consider the {lambda}{phi}{sup 4} theory in detail, but the results appear to hold for a wide class of fields. Although a conventional interpretation of quantum mechanics leads to inconsistency, a path-integral interpretation appears to allow a consistent assignment of probabilities to histories.

• OSTI ID: 7003539
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 46:10; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
FEYNMAN PATH INTEGRAL
FIELD THEORIES
HILBERT SPACE
INTEGRALS
KLEIN-GORDON EQUATION
MATHEMATICAL SPACE
MATRICES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
PHI4-FIELD THEORY
PROBABILITY
PROPAGATOR
QUANTUM FIELD THEORY
QUANTUM MECHANICS
S MATRIX
SCATTERING
SPACE
SPACE-TIME
UNITARITY
WAVE EQUATIONS
WKB APPROXIMATION