

Preprint 73/2016
Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory
Jürgen Tolksdorf and Rainer Verch
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Submission date: 09. Nov. 2016
Pages: 36
published in: Communications in mathematical physics, 357 (2018) 1, p. 319-351
DOI number (of the published article): 10.1007/s00220-017-2943-5
Bibtex
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Abstract:
The D-CTC condition is a condition originally proposed by David Deutsch as
a condition on states of a quantum communication network that contains \backward timesteps"
in some of its branches. It has been argued that this is an analogue for quantum
processes in the presence of closed timelike curves (CTCs). The unusual properties of states
of quantum communication networks that fulfill the D-CTC condition have been discussed
extensively in recent literature. In this work, the D-CTC condition is investigated in the
framework of quantum field theory in the local, operator-algebraic approach due to Haag and
Kastler. It is shown that the D-CTC condition cannot be fulfilled in states which are analytic
for the energy, or satisfy the Reeh-Schlieder property, for a certain class of processes and
initial conditions. On the other hand, if a quantum field theory admits sufficiently many uncorrelated
states across acausally related spacetime regions (as implied by the split property),
then the D-CTC condition can always be fulfilled approximately to arbitrary precision. As
this result pertains to quantum field theory on globally hyperbolic spacetimes where CTCs
are absent, one may conclude that interpreting the D-CTC condition as characteristic for
quantum processes in the presence of CTCs could be misleading, and should be regarded
with caution. Furthermore, a construction of the quantized massless Klein-Gordon field on
the Politzer spacetime, often viewed as spacetime analogue for quantum communication networks
with backward time-steps, is proposed in this work.