Unitary Representations and Osterwalder-Schrader Duality

Details Unitary Representations and Osterwalder-Schrader Duality Unitary Representations and Osterwalder-Schrader Duality

1999-08-06

arxiv.org/abs/math/9908031v1

The Mathematical Legacy of Harish-Chandra: A Celebration of Representation Theory and Harmonic Analysis (R. Doran and V. Varad

Mathematics

Functional Analysis

68 pages; Dedicated to the memory of Irving E. Segal

Scientific paper

The notions of reflection, symmetry, and positivity from quantum field theory are shown to induce a duality operation for a general class of unitary representations of Lie groups. The semisimple Lie groups which have this $c$-duality are identified and they are placed in the context of Harish-Chandra's legacy for the unitary representations program. Our paper begins with a discussion of path space measures, which is the setting where reflection positivity (Osterwalder-Schrader) was first identified as a useful tool of analysis.

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