advanced_notions:minimal_coupling
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| + | ====== Minimal Coupling ====== | ||
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| + | <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: 2017/10/20 13:57 by jakobadmin
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