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Effects of absolute continuity in Feynman's operational calculus
Author(s):
Lance
Nielsen
Journal:
Proc. Amer. Math. Soc.
131
(2003),
781-791.
MSC (2000):
Primary 47A60, 46H30;
Secondary 47A56, 47B38
Posted:
July 17, 2002
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Abstract:
We investigate the effects of having an absolute continuity relation between the time-ordering measures in Feynman's operational calculus. In particular, we obtain some theorems concerning the formation of functions of several noncommuting operators or operator-valued functions under specific absolute continuity assumptions on the time-ordering measures.
References:
-
- 1.
- Defacio, B., Johnson, G.W., and Lapidus, M.L., Feynman's operational calculus and evolution equations. Acta Applicandae Mathematicae 47 (1997), 155 - 211. MR 98f:58050
- 2.
- Feynman, R.P., An operator calculus having applications in quantum electrodynamics, Phys. Rev. 84 (1951), 108-128. MR 13:410e
- 3.
- Jefferies, B., and Johnson, G.W., Feynman's operational calculi for noncommuting operators: definitions and elementary properties, Russ. J. Math. Phys. 8 (2001), to appear.
- 4.
- -, Feynman's operational calcui for noncommuting operators: tensors, ordered support and disentangling an exponential factor, Math. Notes 70 (2001), accepted for publication.
- 5.
- Jefferies, B., Johnson, G.W., and Nielsen, L., Feynman's operational calculi for time-dependent noncommuting operators. J. of Korean Math. Soc. 38 (2001), 193-226. MR 2001m:81154
- 6.
- Johnson, G.W., and Lapidus, M.L., Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman's operational calculus, Mem. Amer. Math. Soc. 62 (1986), 1-78. MR 88f:81034
- 7.
- -, The Feynman Integral and Feynman's Operational Calculus. Oxford Science Publications, Oxford Mathematical Monographs, Oxford Univ. Press, Oxford and New York, 2000. MR 2001i:58015
- 8.
- Johnson, G.W., Nielsen, L., A stability theorem for Feynman's operational calculus, Conference Proc. Canadian Math. Soc.: Conference in honor of Sergio Albeverio's 60th birthday, 2000. MR 2001k:47020
- 9.
- Nielsen, L., Stability Properties for Feynman's Operational Calculus, Ph.D. Dissertation, Mathematics, University of Nebraska, Lincoln, 1999.
- 10.
- Nielsen, L., Stability properties of Feynman's operational calculus for exponential functions of noncommuting operators, submitted for publication.
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Additional Information:
Lance
Nielsen
Affiliation:
Department of Mathematics and Computer Science, Creighton University, Omaha, Nebraska 68178-2090
Email:
lnielsen@creighton.edu
DOI:
10.1090/S0002-9939-02-06592-9
PII:
S 0002-9939(02)06592-9
Keywords:
Functional calculus,
disentangling,
operational calculus
Received by editor(s):
July 10, 2001
Received by editor(s) in revised form:
October 10, 2001
Posted:
July 17, 2002
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2002,
American Mathematical Society
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