Composite particles and symplectic (Semi-) groups

Nuclear composits particle dynamics is intimately related to the fermion character of nucleons. This property is implemented via the permutational structure of nuclear states, leading to the concept of exchange and to the quantum number of the orbital partition. We review Weyl operators and representations of linear canonical transformations in Bargmann Hilbert space. In section 4 we use canonical transformations to describe the general n-body dynamics. In section 5 we derive the composite particle dynamics and discuss an algorithm to obtain the interaction of composite particles whose constituents are assumed to be in harmonic oscillator states. As a first example we treat in section 6 composite particles with unexcited internal oscillator states. In section 7 we deal with composite particles of internal oscillator shell configurations. (orig.)