Physics
Scientific paper
Nov 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phrvd..46.4442f&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 46, Issue 10, 15 November 1992, pp.4442-4455
Physics
17
Theory Of Quantized Fields
Scientific paper
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 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 O(λ3) in a λcphi4 theory, and show how to find the relations to any order. For globally hyperbolic spacetimes the unitarity identities are satisfied [at least to O(λ3)] because of a single property of the configuration-space propagator that reflects the causal structure of the spacetime.
Friedman John L.
Papastamatiou Nicolas J.
Simon Jonathan Z.
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