====== Minimal Coupling ======

<tabbox Why is it interesting?> 

<blockquote>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.<cite> [[https://arxiv.org/pdf/hep-ph/0405147.pdf|Yang-Mills Theory In, Beyond, and Behind Observed Reality]] by  Frank Wilczek</cite></blockquote>

<tabbox Layman> 

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
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<tabbox Student> 

<note tip>
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
</note>
 
<tabbox Researcher> 

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

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<tabbox Examples> 

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<tabbox History> 

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