Why is it interesting?

Why minimal coupling? This requirement arises indirectly, as a consequence of the general difficulty of constructing consistent interacting relativistic quantum field theories in four space-time dimensions. The perturbative construction of such theories involves regularization and renormaliza- tion. If we want to have a closed theory, in which the limiting effect of the regulator can be absorbed into a finite number of renormalization parameters, we must restrict ourselves to renormalizable couplings, that is interaction vertices whose coefficients have non-negative mass dimension (in units with ~ = c = 1, of course). Otherwise the insertion of these vertices will, in general, be accompanied by positive powers of the cutoff mass, and taking that mass to infinity will be counterproductive. This means that the vertices themselves must be constructed from fields whose total mass dimension does not exceed four. This criterion, when combined with gauge invariance, greatly restricts the possibilities, and in particular enforces minimal coupling for the gauge fields. Yang-Mills Theory In, Beyond, and Behind Observed Reality by Frank Wilczek

Layman

Student

Researcher

Common Question 1

Common Question 2

Examples

Example1

Example2:

History