대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제19권4호
  • /
  • Pages.721-730
  • /
  • 2004
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A CONVERGENCE THEOREM FOR FEYNMAN′S OPERATIONAL CALCULUS : THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS

  • 발행 : 2004.10.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Feynman's operational calculus for noncommuting operators was studied via measures on the time interval. We investigate 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.

키워드

참고문헌

  1. P. Billingsley, Convergence of probability measures, Wiley, New York, 1968.
  2. R. Feynman, An operator calculus having application in quantum electrodynamics, Phys. Rev. 84 (1951), 108-128. https://doi.org/10.1103/PhysRev.84.108
  3. B. Jefferies and G. W. Johnson, Feynman's operational calculi for noncommuting operators: Definitions and elementary properties, Russian J. Math. Phys. 8 (2001), 153-178.
  4. B. Jefferies, Feynman's operational calculi for noncommuting operators: Tensors, ordered supports and disentangling an exponential factor, Math. Notes 70 (2001), 744-764. https://doi.org/10.1023/A:1012903732597
  5. B. Jefferies, Feynman's operational calculi for noncommuting operators: Spectral theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), 171-199. https://doi.org/10.1142/S021902570200078X
  6. B. Jefferies, Feynman's operational calculi for noncommuting operators: The monogenic calculus, Adv. Appl. Clifford Algebras 11 (2002), 233-265. https://doi.org/10.1007/BF03042315
  7. B. Jefferies, G. W. Johnson and L. Nielsen, Feynman's operational calculi for time dependent noncommuting operators, J. Korean Math. Soc. 38 (2001), 193-226.
  8. G. W. Johnson and M. L. Lapidus, The Feynman integral and Feynman operational calculus, Oxford U. Press, Oxford, 2000.
  9. G. W. Johnson and M. L. Lapidus, Generalized Dyson series, generalized Feynman diagrams, The Feynman integral and Feynman's operational calculus, Mem. Amer. Math. Soc. 62 (1986), 1-78.
  10. G. W. Johnson and L. Nielsen, A stability theorem for Feynman's operational calculi, Conf. Proc. Canadian Math. Soc. : Conference in honor of Sergio Al-beverio's 60th birthday 29 (2000), 351-365.

피인용 문헌

  1. WEAK CONVERGENCE THEOREMS IN FEYNMAN'S OPERATIONAL CALCULI : THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS vol.25, pp.3, 2012, https://doi.org/10.14403/jcms.2012.25.3.531