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quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...
, the minimal subtraction scheme, or MS scheme, is a particular
renormalization Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering ...
scheme used to absorb the infinities that arise in perturbative calculations beyond
leading order The leading-order terms (or corrections) within a mathematical equation, expression or model are the terms with the largest order of magnitude.J.K.Hunter, ''Asymptotic Analysis and Singular Perturbation Theory'', 2004. http://www.math.ucdavis.edu/~ ...
, introduced independently by
Gerard 't Hooft Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating th ...
and
Steven Weinberg Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic inter ...
in 1973. 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 (\overline), one absorbs the divergent part plus a universal constant that always arises along with the divergence in
Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introdu ...
calculations into the counterterms. When using
dimensional regularization __NOTOC__ In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Fey ...
, i.e. d^4 p \to \mu^ d^d p, it is implemented by rescaling the renormalization scale: \mu^2 \to \mu^2 \frac, with \gamma_ the
Euler–Mascheroni constant Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (). It is defined as the limiting difference between the harmonic series and the natural ...
.


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* * Renormalization group {{statisticalmechanics-stub