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arXiv · 1211.1741

40 Years of Calculus in 4 + epsilon Dimensions

Wolfgang Bietenholz·Lilian Prado
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Abstract

Modern physics describes elementary particles by a formalism known as Quantum Field Theory. However, straight calculations with this formalism lead to numerous divergences, hence one needs a suitable regularization scheme. 40 years ago a surprising scheme was established for this purpose: Dimensional Regularization. One computes in "4 + epsilon space-time dimensions", and takes the limit to our 4 dimensional space-time at the end. This method caused a revolution in particle physics, which led to the Standard Model. Many people refer to its results, and even apply it, without being aware that its history actually started in Latin America, more precisely in La Plata, Argentina. ----- La física moderna describe a las partículas elementales por medio del formalismo conocido como Teoría Cuántica de Campos. Sin embargo, los cálculos directos realizados con este formalismo llevan a una gran cantidad de divergencias, por lo que es necesario un método para regularizarlos. Hace 40 años se estableció un esquema sorprendente para este objetivo: la Regularización Dimensional. Se calcula en "4 + epsilon dimensiones espacio-temporales", y al final se toma el límite a nuestro espacio y tiempo en 4 dimensiones. Este método causó una revolución en la física de partículas, que resultó en el Modelo Estándar. Muchas personas hacen referencia sus resultados, e incluso la aplican, sin saber que su historia comenzó en América Latina, precisamente en La Plata, Argentina.

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Wolfgang Bietenholz, Lilian Prado. 2012-11-08. 40 Years of Calculus in 4 + epsilon Dimensions. https://arxiv.org/abs/1211.1741

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