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In a new theory, the Dirac field can interact with another field, for example with the electromagnetic field in quantum electrodynamics, and the strength of the interaction is measured by a parameter, in the case of QED it is the bare electron charge, <math>e</math>. The general form of the propagator should remain unchanged, meaning that if <math>|\Omega\rangle</math> now represents the vacuum in the interacting theory, the two-point correlation function would now read
:<math> \langle \Omega | T(\psi(x)\bar{\psi}(0))| \Omega \rangle = \int \frac{d^
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 subtraction 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>.
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