Representations of orthogonal and unitary groups, and nuclear models

The foundations of the microscopic theory of the nucleus is expounded based on operator series whose first terms determine the model Hamiltonians. A formulation of the question is given and special features are discussed for the many-body problem in multiparticle quantum systems and anticollective effects of irreducible representations of unitary groups in the derivation of the Hamiltonians of exactly solvable models with strong, bounded dynamics. Traditional and nontraditional approaches to the many-body problem in the theory of the nucleus are compared.