Preprint
Reflection positivity in Euclidean formulations of relativistic quantum mechanics of particles
ArXiV.org
Cornell University
06/25/2025
DOI: 10.48550/arxiv.2506.20526
Abstract
This paper discusses the general structure of reflection positive Euclidean covariant distributions that can be used to construct Euclidean representations of relativistic quantum mechanical models of systems of a finite number of degrees of freedom. Because quantum systems of a finite number of degrees of freedom are not local, reflection positivity is not as restrictive as it is in a local field theory. The motivation for the Euclidean approach is that it is straightforward to construct exactly Poincaré invariant quantum models of finite number of degrees of freedom systems that satisfy cluster properties and a spectral condition. In addition the quantum mechanical inner product can be computed without requiring an analytic continuation. Whether these distributions can be generated by a dynamical principle remains to be determined, but understanding the general structure of the Euclidean covariant distributions is an important first step.
Details
- Title: Subtitle
- Reflection positivity in Euclidean formulations of relativistic quantum mechanics of particles
- Creators
- Gohin Shaikh Samad - McNeese State UniversityW. N Polyzou - University of Iowa
- Resource Type
- Preprint
- Publication Details
- ArXiV.org
- DOI
- 10.48550/arxiv.2506.20526
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 06/25/2025
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984833628902771
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