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Quantization on timelike hypersurfaces in curved spacetime

Banff International Research Station for Mathematical Innovation and Discovery

When investigating quantum or semiclassical phenomena in a general relativistic context one usually resorts to quantum field theory in curved spacetime. However, traditional quantization methods rely on foliating spacetime into spacelike hypersurfaces or on fixing asymptotic boundary conditions in time. This is a serious limitation if for the problem of interest no suitable Cauchy hypersurfaces exist and/or if boundary conditions are naturally given on timelike hypersurfaces, either at finite locations or asymptotically. I will outline methods of quantization adapted to such situations and the conceptual insights on which they are based. If time permits I will comment on how this may contribute to the search for a quantum theory of gravity.

Mathematics; Relativity and gravitational theory; Partial differential equations; Global analysis

video/mp4

Author affiliation: Universidad Nacional Autónoma de México

2020-01-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73431

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/