Parastatistics, highest weight \(\mathrm{osp}(N,\infty)\) modules, singleton statistics and confinement (Q581636)

The basic ideas and latest developments of parastatistics in the modern quantum field theory are reviewed and some generalizations of this approach are suggested. Since the structure of parabose statistics is determined by the infinite dimensional orthosymplectic Lie super algebra \(\mathrm{osp}(N,\infty)\), the Fock spaces of parastatistics are interpreted as the unitarizable highest weight modules with the degenerate highest weight space (vacuum). It is pointed out that the other hermitian representations of \(\mathrm{osp}(1,\infty)\) may be applied for description of symmetry breakdown. The alternative possibilities of using in parastatistics the so called ``extended orthosymplectic'' superalgebras \((N,2n)\) and \((N,\infty)\) are also considered. In conclusion the problems of compositeness and confinement in the framework of singletons (obeying parastatistics) are briefly discussed.