Are there any electric fields associated to the scalar fields in quantum field theory? We know that electric field due to stationary charges is given by gradient of phi.
In quantum field theory the scalar fields associated with bosons doesn't have any electric fields but while dealing with em fields we get vector E as conjugate momenta to A_u. why there are not any electric fields associated to such scalar fields?
 A: I don't quite understand your question, perhaps you can clarify. Also, the boson mediating the electromagnetic interaction is a spin-1 particle, not a scalar which would be spin-0. 
First of all, a electric field and  a field in quantum field theory are not the same thing. The former is a measurable quantity for instance, while the second is a second-quantized field of a classical field theory. In classical electrodynamics the electric field is given by 
$$\vec{E} = - \nabla \phi - \frac{\partial}{\partial t} \vec{A}$$
If we put $\phi$ and $\vec{A}$ together in the 4-vector $A_\mu$ we find the electric fields in the field strength tensor $F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. 
From the $F_{\mu\nu}$ we can construct a classical field theory which if second-quantized correctly (which does lead to some problems) gives quantum electrodynamics QED where we identify the gauge bosons with photons, the quanta of electric fields. Note that we only talk of bosons once we quantize and find a spin-1 particle in the spectrum.
So it is by construction that the electric field is in this way associated to the Lorentz vector $A_\mu$. There are certainly fields associated to other particles such as the scalar Higgs field.
