The force is also F=\frac{dp}{dt} = m\frac{dv}{dt}=ma, and the momentum of photon is p=h\nu. So, the only thing which may vary for a photon is its frequency, \nu.
I think it is required to establish that the claim "momentum of a body can be constant while it accelerates" is valid for a system of bodies and not for the same body, because initial body splits in other bodies, as it accelerates.
In my opinion is a misconception that the initial momentum of a body can be constant while it accelerates.
Let be initial momentun of the body p_1=m_1v_1. The body splites in two bodies, with the momentum p_2 and p_3, so that p_2+p_3=p_1.
If we put the condition p_1=p_2 = constant, then we...
Momentum of a body can be constant while it accelerates? I mean if velocity increases while mass decreases proportional.
And if is true, what force produces acceleration?