On-shell renormalization scheme: Difference between revisions

Revision as of 10:13, 10 August 2012

Revision as of 07:25, 25 August 2012

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:<math> \langle 0 | T(\psi(x)\bar{\psi}(0))| 0 \rangle =iS_F(x) = \int \frac{d^4p}{(2\pi)^4}\frac{ie^{-ip\cdot x}}{p\!\!\!/-m+i\epsilon} </math>

where <math>T</math> is the [[Time ordered#Time ordering|time-ordering operator]], <math>|0\rangle</math> the vacuum in the non interacting theory, <math>\psi(x)</math> and <math>\bar{\psi}(x)</math> the Dirac field and its Dirac adjoint, and where the left handside of the equation is the [[Correlation_function_Correlation function (quantum_field_theoryquantum field theory)|two-point correlation function]] of the Dirac field.

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

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A renormalization prescription is a set of rules that describes what part of the divergences should be in the renormalized quantities and what parts should be in the counterterms. The prescription is often based on the theory of free fields, that is of the behaviour of <math>\psi</math> and A when they do not interact (which corresponds to removing the term <math>e \bar{\psi} \gamma^\mu \psi A_{\mu} </math> in the Lagrangian).

==References==

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* T. Gehrmann, ''[http://www.theorie.physik.uzh.ch/~pfmonni/QFTI_HS10/QFT_Skript.pdf http://www.theorie.physik.uzh.ch/~pfmonni/QFTI_HS10/QFT_Skript.pdf Quantum Field Theory 1]

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