Quantum evolution across singularities

Details Quantum evolution across singularities Quantum evolution across singularities

2007-06-06

arxiv.org/abs/0706.0824v2

JHEP 0804:021,2008

Physics

High Energy Physics

High Energy Physics - Theory

revised with an emphasis on local counterterm subtraction rather than analyticity; version to be submitted for publication

Scientific paper

10.1088/1126-6708/2008/04/021

Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space).

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