Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Handrack, Carl, Salmhofer, Manfred
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7202270974
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