Feynman's vector potential, a physical meaning clue

[Abrain]

Hi everybody!

I'd like to understand the physical meaning of the Feynman's vector potential definition:

$$A_{m}^{(b)}(x) = e_b \int \delta (xb_{\mu}xb^{\mu})db_m(b), \qquad m=0,1,2,3$$

(component m of the vector potential of the particle b at the point x)

Here

- the integration is done over the whole world line of the b particle, parametrized by the invariant parameter b

- $$\delta$$ is the Dirac delta function

- $$xb_{\mu}xb^{\mu}$$ is the 4-norm of $$x - b$$

- So the $$\delta$$ function is non-zero $$\iff x$$ is in the boundary of the light cone of b.

Can you give me any clues?

Thanks!

 

[Abrain]

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