Alternative Modes for Scalar Field Quantization
Al Angew
Oregon State University
Friday, 21 November, 5 PM
318 Willamette Hall, University of Oregon
The work of Manogue, Dray, and Copeland [1] on the quantization of the
massless scalar field on the trousers spacetime reveals the incompleteness of
the plane wave modes in the following sense: in the analysis of the particle
production arising from the topology change, there are solutions of the wave
equation that are orthogonal (with respect to canonical inner product
associated with the wave operator) to every plane wave mode. With the goal of
capturing these modes and their utility, we consider a formalism for the
canonical quantization of the scalar field based on a set of basis modes that
differ from the usual plane wave modes. In particular, the new modes are
indexed by position, as opposed to momentum. We give a
translation between the standard and new formalisms, and we discuss the
generalization of the new formalism to globally hyperbolic spacetimes, as well
as some observations linking it to other curved space quantum field theory
approaches.
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Corinne A Manogue, Tevian Dray, and Ed Copeland,
The Trousers Problem Revisited,
Pramana 30, 279-292 (1988).