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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Time-ordered operators. II
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by Tepper L. Gill
Trans. Amer. Math. Soc. 279 (1983), 617-634
DOI: https://doi.org/10.1090/S0002-9947-1983-0709572-5

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.
References
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Bibliographic Information
  • © Copyright 1983 American Mathematical Society
  • 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