TL;DR
This paper introduces the concept of twist positivity, a property of partition functions in quantum systems with symmetry, linking it to Feynman-Kac measures and particle interpretations.
Contribution
It defines twist positivity, explores its implications for quantum systems, and connects it to fundamental concepts like Feynman-Kac measures and zero-mass limits.
Findings
Twist positivity is characterized by complex conjugate representations.
It relates to the existence of Feynman-Kac measures.
It reflects a particle interpretation of quantum systems.
Abstract
We identify a positivity property for partition functions in quantum systems with a unitary symmetry group, and we call this "twist positivity." The existence of Feynman-Kac measures and the existence of zero-mass limits are both related to this property. Twist positivity arises from the occurrence of complex conjugate representations on an energy eigenspace, and ultimately reflects a particle interpretation of the quantum system.
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