Mid-point technique for calculating divergent integrals - M Abu-Shady (Annals of Mathematics and Physics - Peertechz Publications, 2019)
The appearance of divergent integrals in the different mathematical-phyiscal models is a real problem. This problem represents that the treatment of divergence integrals did not give a unique value for divergent integrals such as [1]. There are different methods for dealing with the divergent integrals such as analytic continuation [2], by regularization [3], by summability methods [4], and by nite part integrals [5,6], and others [7,8]. In these methods, the missing terms have appeared so that no interpretation gives exact results. In this work, we focus on the quark models that deal with strong interactions between quarks inside nucleon. There are different quark models such as the quark sigma model and its extension [9-15] and Nambu and Jona-Lasinio model (NJL) its extension [16-19]. The NJL is taken as a model for the divergent integral [16]. The NJL model has the divergent integral that obtained from Dirac sea to overcome on this problem, Pauli- Villars and the three-momentum cutoff methods are applied such as [20,21].