The beta function is defined as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\beta(\lambda)=M\frac{d}{dM}\lambda[/tex]

If we make the substitution [itex]t=ln(p/M)[/itex] the above equation becomes:

[tex]\beta(\lambda)=-\frac{d}{dt}\lambda[/tex]

Now if we use e.g. the QED beta function

[tex]\beta(e)=\frac{e^3}{12\pi^3}[/tex]

and for [itex]e(p=M)=e_0[/itex] the result is

[tex]e=\frac{e_0}{1+(3e_0/16\pi^2)log(p/M)}[/tex]

which is clearly false.

What am I missing?

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# Calculation of the running coupling

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