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/ 000254795400002 2-s2.0-41949141349 2007PhyU...50.1217P Citation: Popov V S "Feynman disentangling оf noncommuting operators and group representation theory" Phys. Usp. 50 1217–1238 (2007) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Попов В С «Фейнмановский метод распутывания операторов и теория представлений групп» УФН 177 1319–1340 (2007); DOI: 10.3367/UFNr.0177.200712f.1319