Unitarity of interacting fields in curved spacetime

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

DOI:https://doi.org/10.1103/PhysRevD.46.4442· OSTI ID:7030691

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

---

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

On globally hyperbolic spacetimes, each foliation by spacelike hypersurfaces corresponds to a Hamiltonian description of field theory, and unitarity follows formally from the Hermiticity of the Hamiltonian. For a renormalizable theory, unitarity at each order in perturbation theory follows from the corresponding Hermiticity of each term in the time-ordered product of interaction Hamiltonians. For more general spacetimes, one can still use the path integral to obtain a generalized Lehmann-Symanzik-Zimmermann reduction formula for {ital S}-matrix elements and the corresponding perturbative expansion. Unitarity imposes an infinite set of identities on the scattering amplitudes, which are the generalizations of the flat-spacetime Cutkosky rules. We find these explicitly to {ital O}({lambda}{sup 3}) in a {lambda}{ital cphi}{sup 4} theory, and show how to find the relations to any order. For globally hyperbolic spacetimes the unitarity identities are satisfied (at least to {ital O}({lambda}{sup 3})) because of a single property of the configuration-space propagator that reflects the causal structure of the spacetime.

• OSTI ID: 7030691
• 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

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
DIAGRAMS
FEYNMAN DIAGRAM
FIELD THEORIES
HAMILTONIANS
HILBERT SPACE
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRICES
MATRIX ELEMENTS
PERTURBATION THEORY
PROPAGATOR
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RENORMALIZATION
S MATRIX
SCALAR FIELDS
SPACE
SPACE-TIME
UNITARITY