Difficulty with a kinematic concept of unstable particles: the SZ.-Nagy extension and the Matthews-Salam-Zwanziger representation
dc.contributor.author | Williams, David N. | en_US |
dc.date.accessioned | 2006-09-11T17:51:09Z | |
dc.date.available | 2006-09-11T17:51:09Z | |
dc.date.issued | 1971-12 | en_US |
dc.identifier.citation | Williams, David N.; (1971). "Difficulty with a kinematic concept of unstable particles: the SZ.-Nagy extension and the Matthews-Salam-Zwanziger representation." Communications in Mathematical Physics 21(4): 314-333. <http://hdl.handle.net/2027.42/46496> | en_US |
dc.identifier.issn | 1432-0916 | en_US |
dc.identifier.issn | 0010-3616 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/46496 | |
dc.description.abstract | We discuss the possibility of describing unstable systems, or dissipative systems in general, by vectors in a Hilbert space, evolving in time according to some non-unitary group or semigroup of translations. If the states of the unstable or dissipative system are embedded in a larger Hilbert space containing “decay products” as well, so that the time evolution of the system as a whole becomes unitary, we show that the infinitesimal generator necessarily has all energies from minus to plus infinity in its spectrum. This result supplements and extends the well-known fact that a positive energy spectrum is incompatible with a decay law bounded by a decreasing exponential. As an example of both facts, we discuss Zwanziger's irreducible, nonunitary representation of the Poincaré group; and we find its minimal, unitary extension (the Sz.-Nagy construction). The answer provides a mathematically canonical approach to the Matthews-Salam theory of wave functions for unstable, elementary particles, where the spectrum difficulty was already recognized. We speculate on the possibility that the Matthews-Salam-Zwanziger representation might be a strong coupling approximation in the relativistic version of the Wigner-Weisskopf theory, but we have not shown the existence of a physically acceptable model where that is so. | en_US |
dc.format.extent | 1313527 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.subject.other | Physics | en_US |
dc.subject.other | Quantum Physics | en_US |
dc.subject.other | Mathematical and Computational Physics | en_US |
dc.subject.other | Quantum Computing, Information and Physics | en_US |
dc.subject.other | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | en_US |
dc.subject.other | Relativity and Cosmology | en_US |
dc.subject.other | Statistical Physics | en_US |
dc.title | Difficulty with a kinematic concept of unstable particles: the SZ.-Nagy extension and the Matthews-Salam-Zwanziger representation | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | The University of Michigan, Ann Arbor, Mich., USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/46496/1/220_2005_Article_BF01645753.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF01645753 | en_US |
dc.identifier.source | Communications in Mathematical Physics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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