Displaced Fock states and their connection to quasiprobabilities

The properties of the displaced Fock states mod a,n) identical to d(a,a*) mod n), (a complex numbers, D(a,a*) displacement operators, n=0,1,2,. . .) are systematically investigated with emphasis on the connections to the Heisenberg-Weyl group and to its irreducible representations. The displaced Fock states comprise the coherent states mod a) identical to mod a,0) as well as the Fock states mod n)…