Browse > Article
http://dx.doi.org/10.4134/CKMS.2008.23.1.067

BLENDING INSTANTANEOUS AND CONTINUOUS PHENOMENA IN FEYNMAN'S OPERATIONAL CALCULI: THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS  

Ahn, Byung-Moo (DEPARTMENT OF MATHEMATICS SOONCHYNHYANG UNIVERSITY)
Yoo, Il (DEPARTMENT OF MATHEMATICS YONSEI UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.1, 2008 , pp. 67-80 More about this Journal
Abstract
Feynman's operational calculus for noncommuting operators was studied via measures on the time interval. We investigate some properties of Feynman's operational calculi which include a variety of blends of discrete and continuous measures in the time dependent setting.
Keywords
Feynman's operational calculus; disentangling;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
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   DOI
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 and G. W. Johnson, Feynman's operational calculi for noncommuting systems of operators: Tensors, ordered supports and disentangling an exponential factor, Math. Notes 70 (2001), 744-764   DOI
5 B. Jefferies and G. W. Johnson, Feynman's operational calculi for noncommuting operators: Spectral theory, Infinite Dimensional Anal. Quantum Probab. 5 (2002), 171-199   DOI   ScienceOn
6 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
7 G. W. Johnson and M. L. Lapidus, The Feynman Integral and Feynman Operational Calculus, Oxford U. Press, Oxford, 2000
8 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
9 V. P. Maslov, Operational Mathod, Mir, Moscow, 1976
10 V. E. Shatalov, V. E. Sternin, and B. Yu, Methods of Noncommutative Analysis, Walter de Gruyter, Berlin, 1996
11 L. Nielsen, Stability properties for Feynman's operational calculus in the combined continuous/discrete Setting, Acta Appl. Math. 88 (2005), 47-79   DOI
12 G. W. Johnson and L. Nielsen, Blending instantaneous and continuous phenomena in Feynman's operational calculi, Stochastic Analysis and Mathematical Physics (SAMP/ANESTOC2002), World Scientific, Singapore (2004), 229-254
13 M. Reed and B. Simon, Methods of Modern Mathematical Physics. Vol. I, Functional Analysis. Rev. and end. ed., Academic Press, New York, 1980
14 B. Jefferies and G. W. Johnson, Feynman's operational calculi for noncommuting operators: The monogenic calculus, Adv. Appl. Clifford Algebra 11 (2002), 233-265   DOI