In theoretical physics, dimensional regularization is a method introduced by Giambiagi and as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter d, the analytic continuation of the number of spacetime dimensions. It has been argued that Zeta regularization and dimensional regularization are equivalent since they use the same principle of using analytic continuation in order for a series or integral to converge.
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| - Dimensional regularization (en)
- 차원 조절 (ko)
- Regularização dimensional (pt)
- 維度正規化 (zh)
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| - 양자장론에서 차원 조절(次元調節, dimensional regularization)이란 발산하는 적분을 임의의 복소 차원으로 해석적 연속하는, 조절의 한 방법이다. 게이지 대칭을 보존하므로, 게이지 이론에서 유용하다. 독특하게도, 로그적 발산보다 더 큰 발산을 숨긴다. 해석적으로 연속할 수 없는, 레비치비타 기호를 포함한 항(강력의 CP 위반 항 등)에는 적용할 수 없다. (ko)
- Em física teórica, a regularização dimensional é um método introduzido por Giambiagi e para regularizar integrais na avaliação de diagramas de Feynman; em outras palavras, atribuindo valores aos que são funções meromórficas de um , chamado dimensão. (pt)
- 在量子場論中，維度正規化是一種正規化辦法。Giambiagi、Bollini、 杰拉德·特·胡夫特和马丁纽斯·韦尔特曼都提出了這個辦法。物理學家使用維度正規化來計算费曼图的積分。积分的值是d的亞純函數；d是時空的維度。 (zh)
- In theoretical physics, dimensional regularization is a method introduced by Giambiagi and as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter d, the analytic continuation of the number of spacetime dimensions. It has been argued that Zeta regularization and dimensional regularization are equivalent since they use the same principle of using analytic continuation in order for a series or integral to converge. (en)
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| - In theoretical physics, dimensional regularization is a method introduced by Giambiagi and as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter d, the analytic continuation of the number of spacetime dimensions. Dimensional regularization writes a Feynman integral as an integral depending on the spacetime dimension d and the squared distances (xi−xj)2 of the spacetime points xi, ... appearing in it. In Euclidean space, the integral often converges for −Re(d) sufficiently large, and can be analytically continued from this region to a meromorphic function defined for all complex d. In general, there will be a pole at the physical value (usually 4) of d, which needs to be canceled by renormalization to obtain physical quantities. showed that dimensional regularization is mathematically well defined, at least in the case of massive Euclidean fields, by using the Bernstein–Sato polynomial to carry out the analytic continuation. Although the method is most well understood when poles are subtracted and d is once again replaced by 4, it has also led to some successes when d is taken to approach another integer value where the theory appears to be strongly coupled as in the case of the Wilson–Fisher fixed point. A further leap is to take the interpolation through fractional dimensions seriously. This has led some authors to suggest that dimensional regularization can be used to study the physics of crystals that macroscopically appear to be fractals. It has been argued that Zeta regularization and dimensional regularization are equivalent since they use the same principle of using analytic continuation in order for a series or integral to converge. (en)
- 양자장론에서 차원 조절(次元調節, dimensional regularization)이란 발산하는 적분을 임의의 복소 차원으로 해석적 연속하는, 조절의 한 방법이다. 게이지 대칭을 보존하므로, 게이지 이론에서 유용하다. 독특하게도, 로그적 발산보다 더 큰 발산을 숨긴다. 해석적으로 연속할 수 없는, 레비치비타 기호를 포함한 항(강력의 CP 위반 항 등)에는 적용할 수 없다. (ko)
- Em física teórica, a regularização dimensional é um método introduzido por Giambiagi e para regularizar integrais na avaliação de diagramas de Feynman; em outras palavras, atribuindo valores aos que são funções meromórficas de um , chamado dimensão. (pt)
- 在量子場論中，維度正規化是一種正規化辦法。Giambiagi、Bollini、 杰拉德·特·胡夫特和马丁纽斯·韦尔特曼都提出了這個辦法。物理學家使用維度正規化來計算费曼图的積分。积分的值是d的亞純函數；d是時空的維度。 (zh)
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