Quantum Physics, Fields and Closed Timelike Curves: The DCTC Condition in Quantum Field Theory
Abstract
The DCTC condition has originally been 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 DCTC condition have been discussed extensively in recent literature. In this work, the DCTC condition is investigated in the framework of quantum field theory in the local, operatoralgebraic approach due to Haag and Kastler. It is shown that the DCTC condition cannot be fulfilled in states that are analytic in the energy, or satisfy the ReehSchlieder 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 DCTC 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 DCTC 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 KleinGordon field on the Politzer spacetime, often viewed as spacetime analogue for quantum communication networks with backward timesteps, is proposed in this work.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 January 2018
 DOI:
 10.1007/s0022001729435
 arXiv:
 arXiv:1609.01496
 Bibcode:
 2018CMaPh.357..319T
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 pdflatex, 34 pages, 5 figures. Invited contribution to Commun. Math. Phys. Special Issue dedicated to the memory of Rudolf Haag. v2: Typos corrected, reference added