Combinatorics in tensor-integral reduction

作     者：Ee, June-Haak Jung, Dong-Won Kim, U-Rae Lee, Jungil 

作者机构：Korea Univ Dept Phys Seoul 02841 South Korea 

出 版 物：《EUROPEAN JOURNAL OF PHYSICS》 (欧洲物理学学报)

年 卷 期：2017年第38卷第2期

页      面：1-18页

核心收录：

学科分类：0401[教育学-教育学] 07[理学] 0702[理学-物理学] 

基　　金：Global PhD Fellowship Program through the National Research Foundation (NRF) of Korea - Korea government (MOE) [NRF-2012H1A2A1003138] NRF [NRF-2015R1D1A1A01059141] Do-Yak project of NRF [NRF-2015R1A2A1A15054533] 

主　　题：combinatorics tensor angular integral tensor-integral reduction isotropic tensor Feynman integral 

摘      要：We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the n-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one can greatly reduce the efforts to compute cumbersome angular integrals into straightforward combinatoric counts. This method is generalised into the cases in which such symmetries are present in subspaces. We further demonstrate the mechanism of the tensor-integral reduction that is widely used in various physics problems such as perturbative calculations of the gauge-field theory in which divergent integrals are regularised in d = 4 - 2 epsilon space-time dimensions. The main derivation is given in the ndimensional Euclidean space. The generalisation of the result to the Minkowski space is also discussed in order to provide graduate students and researchers with techniques of tensor-integral reduction for particle physics problems.