Noncommutative coordinate picture of the quantum phase space

We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms functions on projective Hilbert space, and its space analog, with a noncommutative product explicit coordinates discuss physical dynamical picture. The isomorphism is then used as base translation differential symplectic geometry infinite dimensional manifolds onto geometry. Hence, we obtain latter from theory itself. have essentially extended formalism Schr̈odinger versus Heisenberg picture which describe mathematically like coordinate map phase presented argument to be seen model coordinated by six position momentum operators. taken formal work formulates intuitive idea that can alternative, coordinate, familiar at least so long concerned.