What is it about?

Quantum field theory (QFT) is an extremely successful theory describing the nature in the microscopic scale. On the other hand general relativity describes gravity in terms of curved spacetime. This paper provides an interesting example of QFT in curved spacetime in a so-called non-globally-hyperbolic spacetime where the dynamics must be determined by specifying boundary conditions at infinity.

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Why is it important?

It is shown that in the spacetime studied in this paper the requirement of invariance under the spacetime symmetries severely restricts the possible boundary conditions at infinity. Moreover, it is found that among the invariant theories there are ones for which the vacuum state is not invariant but transforms nontrivially under spacetime symmetry transformations, which turn out to be so-called Bogoliubov transformations.


I originally thought that our research would lead only to expected results, but it was gratifying to find apparently the first example where spacetime symmetry transformations of the vacuum state are Bogoliubov transformations since this implies that the vacuum state in one coordinate frame is seen to contain particles in other coordinate frames.

Atsushi Higuchi
University of York

Read the Original

This page is a summary of: Scalar field in AdS2 and representations of SL̃(2,R), Journal of Mathematical Physics, December 2022, American Institute of Physics, DOI: 10.1063/5.0117631.
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