Feynman's Operational Calculi for Noncommuting Systems of Operators: Tensors, Ordered Supports, and Disentangling an Exponential Factor
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 815-838.

Voir la notice de l'article provenant de la source Math-Net.Ru

In a recent paper, the authors presented the key ideas involved in their approach to Feynman's operational calculi for systems of not necessarily commuting bounded linear operators acting on a Banach space. The central objects of the theory are the disentangling algebra, a commutative Banach algebra, and the disentangling map which carries this commutative structure into the noncommutative algebra of operators. The study of properties of these disentangling maps will be pursued in this paper with an emphasis on (i) Feynman's formula for disentangling an exponential factor, and (ii) the effect on the disentangling map of ordered supports of some or all of the measures which govern the disentangling.
@article{MZM_2001_70_6_a1,
     author = {B. Jefferies and G. W. Johnson},
     title = {Feynman's {Operational} {Calculi} for {Noncommuting} {Systems} of {Operators:} {Tensors,} {Ordered} {Supports,} and {Disentangling} an {Exponential} {Factor}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {815--838},
     publisher = {mathdoc},
     volume = {70},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a1/}
}
TY  - JOUR
AU  - B. Jefferies
AU  - G. W. Johnson
TI  - Feynman's Operational Calculi for Noncommuting Systems of Operators: Tensors, Ordered Supports, and Disentangling an Exponential Factor
JO  - Matematičeskie zametki
PY  - 2001
SP  - 815
EP  - 838
VL  - 70
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a1/
LA  - ru
ID  - MZM_2001_70_6_a1
ER  - 
%0 Journal Article
%A B. Jefferies
%A G. W. Johnson
%T Feynman's Operational Calculi for Noncommuting Systems of Operators: Tensors, Ordered Supports, and Disentangling an Exponential Factor
%J Matematičeskie zametki
%D 2001
%P 815-838
%V 70
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a1/
%G ru
%F MZM_2001_70_6_a1
B. Jefferies; G. W. Johnson. Feynman's Operational Calculi for Noncommuting Systems of Operators: Tensors, Ordered Supports, and Disentangling an Exponential Factor. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 815-838. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a1/

[1] Feynman R., “An operator calculus having applications in quantum electrodynamics”, Phys. Rev., 84 (1951), 108–128 | DOI | MR | Zbl

[2] Feynman R., “Mathematical formulation of the quantum theory of electromagnetic interaction”, Phys. Rev., 80 (1950), 440–457 | DOI | MR | Zbl

[3] Feynman R., Hibbs A., Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965 | Zbl

[4] Jefferies B., Johnson G. W., “Feynman's operational calculi for noncommuting operators: Definitions and elementary properties”, Russ. J. Math. Phys., 8:2 (2001), 153–178 | MR

[5] Johnson G. W., Lapidus M. L., The Feynman Integral and Feynman's Operational Calculus, Oxford Math. Monograph., Oxford Univ. Press, Oxford, 2000

[6] Maslov V. P., Operatornye metody, Nauka, M., 1973

[7] Nazaikinskii V. E., Shatalov V. E., Sternin B. Yu., Methods of Noncommutative Analysis, Studies in Math., 22, Walter de Gruyter, Berlin–New York, 1996 | MR

[8] Jefferies B., Johnson G. W., Nielsen L., “Feynman's operational calculi for time dependent noncommuting operators”, Proc. of Seoul Conference “Feynman Integral and Applications”; J. Korean Math. Soc., 38 (2001) (to appear)

[9] Nielsen L., Thesis, Univ. of Nebraska, Lincoln, 1999 | Zbl

[10] Johnson G. W., Nielsen L., “A stability theorem for Feynman's operational calculus”, Conference in Honor of Sergio Albeverio's 60th birthday, Conference Proc. Canad. Math. Soc., 29, 2000, 351–365 | Zbl

[11] Jefferies B., Johnson G. W., Feynman's operational calculi for noncommuting systems of operators, Pure Math. Report. PM 98/99, School of Mathematics, UNSW, Sydney, Australia, 1999

[12] Reed M., Simon B., Methods of Modern Mathematical Physics, V. 1, Acad. Press, Orlando, 1980

[13] Anderson R. F. V., “The Weyl functional calculus”, J. Funct. Anal., 4 (1969), 240–267 | DOI | Zbl