advanced_notions:minimal_coupling

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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> | ||

+ | |||

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