A systematic treatment is presented for the transformation matrix elements between different type of basis sets in the SL(2, C) representation space and for the boost matrix elements. The treatment is based on the theory of invariant bilinear functionals and makes use of the knowledge of explicit basis functions. New expressions are given for the SU(2) ↔ E(2) and SU(1, 1) ↔ E(2) overlap functions, and it is shown that they can be considered as a Fourier transform of a function, which is also known. Some relations are proved between boost functions and transformation matrix elements. In the Appendix a new and relatively simple expression is derived for the boost matrix elements djmj′j0σ(ξ) in SU(2) basis.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics