Number operators in a general quon algebra

Abstract

The existence of the number operators Nk in a general quon algebra is proved and a general construction of Nk is presented. A new general simple structure of Nk is proved when mod qij mod <1, For all i, j in S. General recurrent relations for the corresponding coefficients are constructed and solved in special cases. These solutions are discussed and a conjecture for a general solution is proposed. Cases in which some or all mod qij mod =1 are discussed.