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A Convergence Theorem for Feynman's Operational Calculus : The case ofTime dependent noncommuting operators

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Feynman's operational calculus for noncommuting op- erators was studied via measures on the time interval. We investi- gate that if a sequence of p-tuples of measures converges to another p-tuple of measures, then the corresponding sequence of operational calculi in the time dependent setting converges to the operational calculus determined by the limiting p-tuple of measures.

Abstract

Feynman's operational calculus for noncommuting op- erators was studied via measures on the time interval. We investi- gate that if a sequence of p-tuples of measures converges to another p-tuple of measures, then the corresponding sequence of operational calculi in the time dependent setting converges to the operational calculus determined by the limiting p-tuple of measures.

참고문헌 (9)

  1. "Convergence of probability measures" (1968)
  2. "An operator calculus having application in quantum electrodynam-ics" (1951)
  3. "Feynman's operational calculi for noncommut-ing operators", 8, pp.153~178 (2001)
  4. "Feynman's operational calculi for noncommuting operators", 70, pp.744~764 (2001)
  5. "Feynman's operational calculi for noncommuting operators", 5, pp.177~199 (2002)
  6. "Feynman's operational calculi for noncommuting operators", 11, pp.233~265 (2002)
  7. "Feynman's operational calculi for time dependent noncommuting operators", 38, pp.193~226 (2001)
  8. "The Feynman integral and Feynman opera-tional calculus" (2000), Oxford U. Press
  9. "A stability theorem for Feynman's operational calculi", 29, pp.351~365 (2000)

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