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BLENDING INSTANTANEOUS AND CONTINUOUS PHENOMENA IN FEYNMAN`S OPERATIONAL CALCULI: THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS
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 Title & Authors
BLENDING INSTANTANEOUS AND CONTINUOUS PHENOMENA IN FEYNMAN`S OPERATIONAL CALCULI: THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS
Ahn, Byung-Moo; Yoo, Il;
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 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;
 Language
English
 Cited by
1.
WEAK CONVERGENCE THEOREMS IN FEYNMAN'S OPERATIONAL CALCULI : THE CASE OF TIME DEPENDENT NONCOMMUTING OPERATORS, Journal of the Chungcheong Mathematical Society, 2012, 25, 3, 531  crossref(new windwow)
 References
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 crossref(new window)

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 crossref(new window)

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 crossref(new window)

6.
B. Jefferies and G. W. Johnson, Feynman's operational calculi for noncommuting operators: The monogenic calculus, Adv. Appl. Clifford Algebra 11 (2002), 233-265 crossref(new window)

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, Blending instantaneous and continuous phenomena in Feynman's operational calculi, Stochastic Analysis and Mathematical Physics (SAMP/ANESTOC2002), World Scientific, Singapore (2004), 229-254

11.
V. P. Maslov, Operational Mathod, Mir, Moscow, 1976

12.
V. E. Shatalov, V. E. Sternin, and B. Yu, Methods of Noncommutative Analysis, Walter de Gruyter, Berlin, 1996

13.
L. Nielsen, Stability properties for Feynman's operational calculus in the combined continuous/discrete Setting, Acta Appl. Math. 88 (2005), 47-79 crossref(new window)

14.
M. Reed and B. Simon, Methods of Modern Mathematical Physics. Vol. I, Functional Analysis. Rev. and end. ed., Academic Press, New York, 1980