| Revision as of 20:33, 12 December 2006 editMaliz (talk | contribs)304 edits categorize← Previous edit | Revision as of 06:49, 30 June 2009 edit undoA.K.Nole (talk | contribs)563 edits Example using excellent text from Butcher groupNext edit → | ||
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| In the similar and more widely used '''modified minimal subtraction''', or '''MS-bar scheme''', one absorbs the divergent part plus a universal constant (which always arises along with the divergence in ] calculations) into the counterterms. | In the similar and more widely used '''modified minimal subtraction''', or '''MS-bar scheme''', one absorbs the divergent part plus a universal constant (which always arises along with the divergence in ] calculations) into the counterterms. | ||
| ==Example== | |||
| {{main|Butcher group}} | |||
| An example of the minimal subtraction scheme may be found in the formalism associated to the ], where the ''Feynman rules'' are given by a homomorphism taking values in the algebra ''V'' of ] in ''z'' with poles of finite order and the ''renormalization scheme'' is given by a linear operator ''R'' on ''V'' such that ''R'' satisfies the ] <math>R(fg) + R(f)R(g) = R(fR(g)) + R(R(f)g)</math> and the image of ''R'' – ''id'' lies in the algebra ''V''<sub>+</sub> of ] in ''z''. | |||
| In this context the minimal subtraction scheme may be expressed as taking the ] | |||
| :<math>\displaystyle R(\sum_{n} a_n z^n )= \sum_{n< 0} a_n z^n.</math> | |||
| {{particle-stub}} | {{particle-stub}} | ||
Revision as of 06:49, 30 June 2009
In quantum field theory, the minimal subtraction scheme, or MS scheme is a particular renormalization scheme used to absorb the infinities that arise in perturbative calculations beyond leading order. The MS scheme consists of absorbing only the divergent part of the radiative corrections into the counterterms.
In the similar and more widely used modified minimal subtraction, or MS-bar scheme, one absorbs the divergent part plus a universal constant (which always arises along with the divergence in Feynman diagram calculations) into the counterterms.
Example
Main article: Butcher groupAn example of the minimal subtraction scheme may be found in the formalism associated to the Butcher group, where the Feynman rules are given by a homomorphism taking values in the algebra V of Laurent series in z with poles of finite order and the renormalization scheme is given by a linear operator R on V such that R satisfies the Rota-Baxter identity and the image of R – id lies in the algebra V+ of power series in z.
and the image of R – id lies in the algebra V+ of In this context the minimal subtraction scheme may be expressed as taking the principal part
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