Minimal subtraction scheme (original) (raw)

From Wikipedia, the free encyclopedia

Renormalization scheme in quantum field theory

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, introduced independently by Gerard 't Hooft and Steven Weinberg in 1973.[1][2] 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 (MS), one absorbs the divergent part plus a universal constant that always arises along with the divergence in Feynman diagram calculations into the counterterms. When using dimensional regularization, i.e. d 4 p → μ 4 − d d d p , {\displaystyle \ \mathrm {d} ^{4}p\to \mu ^{4-d}\mathrm {d} ^{d}p\ ,} {\displaystyle \ \mathrm {d} ^{4}p\to \mu ^{4-d}\mathrm {d} ^{d}p\ ,} it is implemented by rescaling the renormalization scale: μ 2 → μ 2 e γ E 4 π , {\displaystyle \ \mu ^{2}\to \mu ^{2}{\frac {e^{\gamma _{\mathrm {E} }}}{4\ \pi }}\ ,} {\displaystyle \ \mu ^{2}\to \mu ^{2}{\frac {e^{\gamma _{\mathrm {E} }}}{4\ \pi }}\ ,} with the Euler–Mascheroni constant, γ E . {\displaystyle \ \gamma _{\mathrm {E} }\ .} {\displaystyle \ \gamma _{\mathrm {E} }\ .}

  1. ^ 't Hooft, G. (1973). "Dimensional regularization and the renormalization group" (PDF). Nuclear Physics B. 61: 455–468. Bibcode:1973NuPhB..61..455T. doi:10.1016/0550-3213(73)90376-3.
  2. ^ Weinberg, S. (1973). "New approach to the renormalization group". Physical Review D. 8 (10): 3497–3509. Bibcode:1973PhRvD...8.3497W. doi:10.1103/PhysRevD.8.3497.