Modifying the Fine Structure Constant to Incorporate Self-Energy Interactions?

[Lapidus]

How do (e^2)/(4Pi x epsilon x Planck constant x speed of light) cancel to give one and make the fine structure constant dimensionless?

thanks

 

[Bill_K]

The Coulomb energy is V = e²/r, so e² has dimensions of energy*length. On the other hand, h-bar*c = 197.5 MeV-f also has dimensions of energy*length, so the ratio of the two expressions is dimensionless.

 

[RedX]

Does anyone know if by making the fine structure a function of energy, can one capture the Lorentz force as proportional to:

$$\frac{\alpha(s)}{s}$$

where s is a Mandelstam variable and $$\alpha$$ is the fine-structure constant?

Or does one have to resort to:

$$\frac{\alpha(s)}{s-\pi(s)}$$

where $$\pi$$ is the electromagnetic interaction of the photon with itself (the self-energy)?

Can one modify the fine structure constant to incorporate $$\pi(s)$$ by defining the new fine structure constant $$\alpha'(s)$$ as the value that makes the following equation true:

$$\frac{\alpha'(s)}{s}=\frac{\alpha(s)}{s-\pi(s)}$$