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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Time-ordered operators. II


Author: Tepper L. Gill
Journal: Trans. Amer. Math. Soc. 279 (1983), 617-634
MSC: Primary 47D05; Secondary 35K22, 81C35
DOI: https://doi.org/10.1090/S0002-9947-1983-0709572-5
MathSciNet review: 709572
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Abstract: In this paper, we substantially improve on the work of [G1]. After constructing the general mathematical foundations for linear time-ordered evolution equations, we apply our results to show that both the perturbation expansion and the Feynman diagram method are mathematically sound. We provide a remainder term so that the expansion may be considered exact at all orders. We then show that time-ordered operators naturally induce an operator-valued path integral whenever a transition kernel is given.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0709572-5
Article copyright: © Copyright 1983 American Mathematical Society