Feynman disentangling îf noncommuting operators and group representation theory
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
à harmonic oscillator by an external force and/or bó time-varying frequency; spin rotation in à time-varying magnetic field; the disentangling of àn atom (ion) Hamiltonian in à laser field; à 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 à
quantum oscillator in analytic form without cumbersome calculations. The case of à D-dimensional oscillator is briefly discussed, in particular, in application to the problem of vacuum pair creation in an intense electric field.