### Abstract

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 d_{jmj′}
^{j0σ}(ξ) in SU(2) basis.

Original language | English |
---|---|

Pages (from-to) | 853-860 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 12 |

Issue number | 5 |

Publication status | Published - 1971 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*12*(5), 853-860.

**SL(2, C) Representations in explicitly "energy-dependent" Basis. II.** / Szegö, K.; Tóth, K.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 12, no. 5, pp. 853-860.

}

TY - JOUR

T1 - SL(2, C) Representations in explicitly "energy-dependent" Basis. II

AU - Szegö, K.

AU - Tóth, K.

PY - 1971

Y1 - 1971

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36849110336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849110336&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36849110336

VL - 12

SP - 853

EP - 860

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 5

ER -