On-shell renormalization scheme: Difference between revisions

Revision as of 07:25, 25 August 2012

Revision as of 09:42, 22 October 2012

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Two new quantities have been introduced. First the renormalized mass <math>m_r</math> has been defined as the pole in the Fourier transform of the Feynman propagator. This is the main prescription of the on-shell renormalization scheme (there is then no need to introduce other mass scales like in the minimal substraction scheme). The quantity <math>Z_2</math> represents the new strength of the Dirac field. As the interaction is turned down to zero by letting <math>e\rightarrow 0</math>, these new parameters should tend to a value so as to recover the propagator of the free fermion, namely <math>m_r\rightarrow m</math> and <math>Z_2\rightarrow 1</math>.

This means that <math>m_r</math> and <math>Z_2</math> can be defined as a serieseries in <math>e</math> if this parameter is small enough (in the unit system where <math>\hbar=c=1</math>, <math>e=\sqrt{4\pi\alpha}\simeq 0.3</math>, where <math>\alpha</math> is the [[fine-structure constant]]). Thus these parameters can be expressed as

:<math>Z_2=1+\delta_2</math>