- 學位論文
超對稱自旋多項式與雅可比函數
Supersymmetric spinning polynomials in 4D and recurrence relation of Jacobi polynomials
並列摘要
Spinning Gegenbauer polynomials provide us orthogonal basis of on- shell tree amplitude with massive spin propagating between 4 massless par- ticle in 4D. In this thesis, we describe the residue of N = 1 supersymmetric 4 massless vertex with mass, scattering angle, and Grassmann variable, re- ferred to supersymmetric N = 1 spinning polynomials. And these can be expanded to spinning Gegenbauer polynomials. This helps us split different spin of components of massive supermultiplet out of supersymmetric spin- ning polynomials. In general, expansion coefficients are derived from inner product of this residue with each orthogonal basis over normalized constant. While supersymmetric spinning polynomials are not pure Jacobi polynomials (orthonormal special functions). We can’t compute the expansion coefficients before constructing orthonormal basis of them. This paper provide another idea of expansion computation. Following the recurrence relation, property of Jacobi polynomials, each algebraic Jacobi polynomial is split to two or more. Therefore,component of residue of N = 1 supersymmetric 4 mass- less vertex can be split to different spinning Gegenbauer polynomials with expansion coefficients.