Evolution in quantum causal histories
Abstract
We provide a precise definition and analysis of quantum causal histories (QCHs). A QCH consists of a discrete, locally finite, causal prespacetime with matrix algebras encoding the quantum structure at each event. The evolution of quantum states and observables is described by completely positive maps between the algebras at causally related events. We show that this local description of evolution is sufficient and that unitary evolution can be recovered wherever it should actually be expected. This formalism may describe a quantum cosmology without an assumption of global hyperbolicity; it is thus more general than the Wheeler De Witt approach. The structure of a QCH is also closely related to quantum information theory and algebraic quantum field theory on a causal set.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 August 2003
 DOI:
 10.1088/02649381/20/16/320
 arXiv:
 arXiv:hepth/0302111
 Bibcode:
 2003CQGra..20.3839H
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 20 pages. 8 figures. (v3: minor corrections, additional references [2,3]) to appear in CQG