Abstract
The construction of an indirect interaction operator for the particles of one physical subsystem via the quasiparticles of another subsystem consists of two steps: an automorphic mapping of the Hamiltonian defined in the Hilbert space of the problem under consideration and the averaging over the quasipartical degrees of freedom. Generalization of the automorphic mappings to the class of the homomorphic mappings is introduced here. The expressions for the potentials of the indirect spin interaction via the phonon field, which do not contain improper integrals as arguments, are found within this approach. Thus the derived theory is free from the arbitrariness connected with the approximate calculation of the improper integrals.
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