New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural and important extension of Fan's paper (Fan Hong-Yi 2010 Chin. Phys. B 19 040305) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator \Delta(\mu, \nu) (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to (a^\dagger_1-a_2) and (a_1+a^\dagger_2) can be solved and the contents of phase space quantum mechanics can be enriched, where a_i, a_i^\dagger are bosonic creation and annihilation operators, respectively.