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

Ahn, Byung-Moo    (Department of Mathematics Soonchynhyang University   ); Lee, Choon-Ho    (Department of Mathematics Hoseo University  );
  • 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.


  • 주제어

    Feynman′s operational calculus .   disentangling.  

  • 참고문헌 (10)

    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. 
    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. 
    5. B. Jefferies, Feynman's operational calculi for noncommuting operators: Spectral theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), 171-199. 
    6. B. Jefferies, Feynman's operational calculi for noncommuting operators: The monogenic calculus, Adv. Appl. Clifford Algebras 11 (2002), 233-265. 
    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. 

 저자의 다른 논문

  • Lee, Choon-Ho (10)

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    2. 1997 "SUFFICIENT CONDITIONS ON THE EXISTENCE OF SELFSIMILAR SOLUTIONS FOR NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS" 충청수학회지 = Journal of the Chungcheong Mathematical Society 10 (1): 71~85    
    3. 1998 "THE RIEMANN PROBLEM FOR A SYSTEM OF CONSERVATION LAWS OF MIXED TYPE (II)" Communications of the Korean Mathematical Society = 대한수학회논문집 13 (1): 37~59    
    4. 1999 "EXISTENCE OF SOLUTIONS FOR THE NONLINEAR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN SEVERAL SPACE VARIABLES" 충청수학회지 = Journal of the Chungcheong Mathematical Society 12 (1): 73~93    
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