Unitarity of Quantum Theory and Closed Time-Like Curves

Details Unitarity of Quantum Theory and Closed Time-Like Curves Unitarity of Quantum Theory and Closed Time-Like Curves

1994-09-26

arxiv.org/abs/hep-th/9409156v3

Phys.Rev.D52:5773-5782,1995

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTeX. Final revised paper to be published in Phys Rev D. Some changes are made to expand our discussion of Anderson

Scientific paper

10.1103/PhysRevD.52.5773

Interacting quantum fields on spacetimes containing regions of closed timelike curves (CTCs) are subject to a non-unitary evolution $X$. Recently, a prescription has been proposed, which restores unitarity of the evolution by modifying the inner product on the final Hilbert space. We give a rigorous description of this proposal and note an operational problem which arises when one considers the composition of two or more non-unitary evolutions. We propose an alternative method by which unitarity of the evolution may be regained, by extending $X$ to a unitary evolution on a larger (possibly indefinite) inner product space. The proposal removes the ambiguity noted by Jacobson in assigning expectation values to observables localised in regions spacelike separated from the CTC region. We comment on the physical significance of the possible indefiniteness of the inner product introduced in our proposal.

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