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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Time-ordered operators. I. Foundations for an alternative view of reality


Author: Tepper L. Gill
Journal: Trans. Amer. Math. Soc. 266 (1981), 161-181
MSC: Primary 47D05; Secondary 22E65, 81C99
MathSciNet review: 613790
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Abstract: The purpose of this paper is to present the proper framework for the mathematical foundations of time-ordered operators. We introduce a new mathematical process which we call the chronological process. This process generalizes the notion of a limit and allows us to recapture many properties lost in time-ordering. We then construct time-ordered integrals and evolution operators. We show that under reasonable assumptions, the time-ordered sum of two generators of contraction semigroups is a generator. This result resolves a question that has been debated in physics for forty years.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0613790-2
PII: S 0002-9947(1981)0613790-2
Article copyright: © Copyright 1981 American Mathematical Society