Reflection positivity in Euclidean formulations of relativistic quantum mechanics of particles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911021894991872 |
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| author | Samad, Gohin Shaikh Polyzou, W. N. |
| author_facet | Samad, Gohin Shaikh Polyzou, W. N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reflection positivity in Euclidean formulations of relativistic quantum mechanics of particles Samad, Gohin Shaikh Polyzou, W. N. High Energy Physics - Theory Mathematical Physics Nuclear Theory 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. |
| title | Reflection positivity in Euclidean formulations of relativistic quantum mechanics of particles |
| topic | High Energy Physics - Theory Mathematical Physics Nuclear Theory |
| url | https://arxiv.org/abs/2506.20526 |