An angle at each point in spacetime and A_μ?

Suppose we have a field that is represented at each point in space by an angle that is a function of time, θ(X,t).

Can we make the following identification with the electromagnetic vector potential A_μ(X,t) of a moving point charge with velocity v_x, v_y, and v_z?

θ(X,t) = A_0(X,t),
v_xθ(X,t) = A_x(X,t),
v_yθ(X,t) = A_y(X,t),
v_zθ(X,t) = A_z(X,t)?

Can we think of A_μ as a massless field with each point X of the field constrained to move on a circle (circle in some hidden space)?

Thanks for any help!