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Euclidean formulation of relativistic quantum mechanics of N particles

Journal Article · · Physical Review C
 [1];  [2]
  1. Univ. of Iowa, Iowa City, IA (United States); University of Iowa
  2. Univ. of Iowa, Iowa City, IA (United States)
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A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at subhadronic distance scales. While direct interaction approaches to relativistic quantum mechanics have proved to be useful, they have two disadvantages. One is that cluster properties are difficult to realize for systems of more than two particles. The second is that the relation to quantum field theories is indirect. Euclidean formulations of relativistic quantum mechanics provide an alternative representation that does not have these difficulties. More surprising, the theory can be formulated entirely in the Euclidean representation without the need for analytic continuation. In this work a Euclidean representation of a relativistic N-particle system is discussed. Kernels for systems of N free particles of any spin are given and shown to be reflection positive. Explicit formulas for generators of the Poincaré group for any spin are constructed and shown to be self-adjoint on the Euclidean representation of the Hilbert space. The structure of correlations that preserve both the Euclidean covariance and reflection positivity is discussed.

Research Organization:
Univ. of Iowa, Iowa City, IA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0016457
OSTI ID:
1832096
Journal Information:
Physical Review C, Journal Name: Physical Review C Journal Issue: 2 Vol. 103; ISSN 2469-9985
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS