Relativistic Spherical Functions on the Lorentz Group

Details Relativistic Spherical Functions on the Lorentz Group Relativistic Spherical Functions on the Lorentz Group

2005-07-21

arxiv.org/abs/math-ph/0507056v2

J. Phys. A: Math. Gen. 39, 805-822 (2006)

Physics

Mathematical Physics

21 pages

Scientific paper

10.1088/0305-4470/39/4/006

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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