What's the formula for the amplitude of a photon?
The amplitude at a particular point is a complex number whose squared modulus gives you the probability of finding the particle at that point. This number is also called the "wave function" or "state vector" depending on how you like to express it.Then I should provide a clear context to my question:
By “amplitude of a photon”, I mean the amplitude of probability for a photon situated in a point A of the space A(xA,yA,zA) at t=T1 to appear in an other point B(xB,yB,zB) at t=T2.
Indeed, I read (QED: The strange theory of light and matter) that we could not consider that a photon travelled in a straight line and therefore, we must consider all the potential ways the photon could take.
Besides, a photon has also amplitudes to travel faster or lower than the speed c. These amplitudes reduce each other to zero in long distances, but they must be taken in consideration for short distances.
I guess this problem is in relation with path integrals, but I also read that the amplitude of a photon had a simple expression that depends on (xA-xB)^2, (yA-yB)^2,(zA-zB)^2 and (T1-T2)^2: I’m looking for this expression.
Thanks for your help.