MANY-PARTICLE QUANTUM STATISTICS AND CO-ALGEBRA

Duplication of the space of states, peculiar of Thermo-field Dynamics, is related to fundamental physical concepts such as the idea of ''iso lated system''. By a correct mathematical description of such doubling of the Pock space in terms of co-algebra, the algebra h(1) and its qu antum deformation h(q)(1) are shown to pertain to classical objects ra ther than to bosons, which are instead properly described by su(1, 1). In addition new statistics are introduced, connected to the graded al gebra osp(1\2) and the q-algebras su(q)(1, 1) and osp(q)(1\2).