Lorentz群上的相对论球函数
Relativistic Spherical Functions on the Lorentz Group
摘要：
洛伦兹群的不可约表示的矩阵元计算的基础上，复杂的角动量。结果表明，拉普拉斯-贝尔特拉米算子，在此基础上定义，引起Fuchsian微分方程。利用广义球函数的加法定理，得到了洛伦兹群的矩阵元的一种显式形式。对于洛伦兹群的主级数和补级数的有限维表示和酉表示，给出了矩阵元的不同表示，并给出了超几何函数的形式。
英文摘要：
Matrix elements of irreducible representations of the Lorentz group are calculated on the basis of complex angular momentum. It is shown that Laplace-Beltrami operators, defined in this basis, give rise to Fuchsian differential equations. An explicit form of the matrix elements of the Lorentz group has been found via the addition theorem for generalized spherical functions. Different expressions of the matrix elements are given in terms of hypergeometric functions both for finite-dimensional and unitary representations of the principal and supplementary series of the Lorentz group.
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