Methodological notes

Feynman disentangling f noncommuting operators and group representation theory

Russian Federation State Scientific Center A.I. Alikhanov Institute ofTheoretical 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  harmonic oscillator by an external force and/or b time-varying frequency; spin rotation in  time-varying magnetic field; the disentangling of n atom (ion) Hamiltonian in  laser field;  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  quantum oscillator in analytic form without cumbersome calculations. The case of  D-dimensional oscillator is briefly discussed, in particular, in application to the problem of vacuum pair creation in an intense electric field.

Fulltext is available at IOP
PACS: 02.20.−a, 03.65.Ca, 03.65.Fd (all)
DOI: 10.1070/PU2007v050n12ABEH006401
Citation: Popov V S "Feynman disentangling f noncommuting operators and group representation theory" Phys. Usp. 50 1217–1238 (2007)
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:    «   » 177 1319–1340 (2007); DOI: 10.3367/UFNr.0177.200712f.1319

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