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advanced_notions:minimal_coupling [2017/12/04 07:01] (current)
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 +====== 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.
 +</​note>​
 +  ​
 +<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>​
 +
 +--> Common Question 1#
 +
 + 
 +<--
 +
 +--> Common Question 2#
 +
 + 
 +<--
 +  ​
 +<tabbox Examples> ​
 +
 +--> Example1#
 +
 + 
 +<--
 +
 +--> Example2:#
 +
 + 
 +<--
 +  ​
 +<tabbox History> ​
 +
 +</​tabbox>​
 +
  
advanced_notions/minimal_coupling.txt ยท Last modified: 2017/12/04 07:01 (external edit)