Feynman disentangling оf noncommuting operators and group representation theory

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.