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An angle at each point in spacetime and A_μ?

  1. Mar 22, 2013 #1
    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!
     
  2. jcsd
  3. Mar 22, 2013 #2
    I think this works,

    "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)?"

    I think something is wrong with this,

    "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)?"

    I'm confused, maybe my brain needs food?
     
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