Feynman's method for disentangling noncommuting operators is discussed and applied to nonstationary problems in quantum mechanics, including the excitation of a harmonic oscillator by an external force and/or by time-varying frequency; spin rotation in a time-varying magnetic field; the disentangling of an atom (ion) Hamiltonian in a laser field; a 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 a quantum oscillator in analytic form without cumbersome calculations. The case of a D-dimensional oscillator is briefly discussed, in particular, in application to the problem of vacuum pair creation in an intense electric field.
We introduce a Grassmannian version of the Stratonovich-Hubbard transformation and derive a new functional-integral representation for the grand partition function F (β) of many-fermion N -particle systems. A new separable form for Z (β) is found using both a disentangling method for "the evolution operator" and the dynamical super-Weyl group SW ( N ). Employing fermionic coherent states the relevant trace is calculated exactly. The case of a separable potential is analyzed in some detail.