Quote by plasmon
Is it correct to express quantum field theory as "operator valued function" or "operator function" to spacetimepoints. Also, how value of field at each point act as a seperate degrees of freedom.

A quantum field is an operatorvalued distribution. In many cases (in the relativistic case always) it is too singular to be a function. The separate degrees of freedom are not at a spacetime point but (depending on the representation used) either at each point in a 3space defined by a fixed time, or at a point on a mass shell in momentum space.