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arXiv · 1812.00926

Complex Structures for Klein-Gordon Theory on Globally Hyperbolic Spacetimes

Albert Much·Robert Oeckl
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Abstract

We develop a rigorous method to parametrize complex structures for Klein-Gordon theory in globally hyperbolic spacetimes that satisfy a completeness condition. The complex structures are conserved under time-evolution and implement unitary quantizations. They can be interpreted as corresponding to global choices of vacuum. The main ingredient in our construction is a system of operator differential equations. We provide a number of theorems ensuring that all ingredients and steps in the construction are well-defined. We apply the method to exhibit natural quantizations for certain classes of globally hyperbolic spacetimes. In particular, we consider static, expanding and Friedmann-Robertson-Walker spacetimes. Moreover, for a huge class of spacetimes we prove that the differential equation for the complex structure is given by the Gelfand-Dikki equation.

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Albert Much, Robert Oeckl. 2018-12-03. Complex Structures for Klein-Gordon Theory on Globally Hyperbolic Spacetimes. https://doi.org/10.1088/1361-6382%2Fac3fbd

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