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arXiv · 2608.10685

Reflection Positivity in Free Fermionic Theories

Carl Handrack·Manfred Salmhofer
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Abstract

Reflection positivity is one of the Osterwalder--Schrader axioms for Euclidean quantum field theory, ensuring that the reconstructed relativistic Hilbert space carries a positive-definite inner product. For free fermionic theories whose covariance is a real rational function of the Dirac operator, we prove that reflection positivity holds if and only if all poles are real, simple, and carry non-negative residues. We also explicitly show the failure of reflection positivity for covariances with exponential regulators.

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Carl Handrack, Manfred Salmhofer. 2026-08-11. Reflection Positivity in Free Fermionic Theories. https://arxiv.org/abs/2608.10685

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