Diagonal Representation of Density Matrix Using q-Coherent States

A diagonal representation of the quantum mechanical density matrix by means of standard bosonic oscillator coherent states was obtained by Sudarshan [1] and Glauber [2]. A remarkable feature of this representation is that the average expectation value of normal ordered operators becomes the same as that of a classical function for a probability distribution over complex plane, thereby bringing one-to-one correspondence between classical complex representation and quantum mechanical density matrices. The study of Quantum Groups has led to a nonlinear realization of Lie algebras and this resulted in the construction of SUq(2) algebra using q-bosonic oscillators by Macfarlane [3] and Biedenharn [4]. A corresponding q-fermion oscillator and SUq(2) algebra had been proposed by Parthasarathy and Viswanathan [5]. Such q-oscillators effectively deal with non-ideal systems which have interactions and provide a method to study non-linear excitations of EM fields. The use of q-bosonic oscillator to describe density matrix has been made by Nelson and Fields [6]. In this contribution, we reconsider this issue in more detail and present some new results regarding the self-reproducing property and relation between the expansion coefficients of the density matrix in the Fock space description and q-coherent state description.