Feynman disentangling оf noncommuting operators and group representation theory

V.S. Popov
Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

Feynman’s method for disentangling noncommuting operators is discussed and applied to nonstationary problems in quantum mechanics, including the excitation of а harmonic oscillator by an external force and/or bу time-varying frequency; spin rotation in а time-varying magnetic field; the disentangling of аn atom (ion) Hamiltonian in а laser field; а model with the hidden symmetry group of the hydrogen atom; and the theory of coherent states. The Feynman operator calculus combined with simple group-theoretical considerations allows disentangling the Hamiltonian and obtaining exact transition probabilities between the initial and final states of а quantum oscillator in analytic form without cumbersome calculations. The case of а D-dimensional oscillator is briefly discussed, in particular, in application to the problem of vacuum pair creation in an intense electric field.

PACS: 02.20.−a, 03.65.Ca, 03.65.Fd (all)
DOI: 10.1070/PU2007v050n12ABEH006401
URL: https://ufn.ru/en/articles/2007/12/b/
Web of Science

000254795400002
Scopus

2-s2.0-41949141349
ADS NASA

2007PhyU...50.1217P
Citation: Popov V S "Feynman disentangling оf noncommuting operators and group representation theory" Phys. Usp. 50 1217–1238 (2007)

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Оригинал: Попов В С «Фейнмановский метод распутывания операторов и теория представлений групп» УФН 177 1319–1340 (2007); DOI: 10.3367/UFNr.0177.200712f.1319

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