Multi-mode q-oscillator algebras with q2(k+1)=1 and related thermo field dynamics
Multi—mode q—oscillator algebras with q^2（k＋1）=1 and related thermo field dynamics

A type of multi-mode q-oscillator algebra with q2(k+1)=1 is set up and the associated qk-thermo field dynamics is constructed for all k=1,2,…,∞ in a unified form. It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics (axiomatized form for statistical physics). This means that we obtain infinitely many realizations of the algebraic scheme, which extend the consideration of Ojima 1981 Ann. Phys. 137 1] and contain the usual thermo field dynamics for the fermionic (k=1) and bosonic (k=∞) systems as special cases. As simple applications, the qk-statistical average of some operators are given.