### Abstract

Unitary and nonunitary representations of the SL(2, C) group are investigated in such a basis, in which the subgroup diagonalized is that one which in the four-dimensional representation leaves invariant the 4-vector p_{μ} = (1/2(1 + ν), 0, 0, 1/2(1 - ν)) for an arbitrary real value of p_{μ}
^{2} = ν. The split of the representation space into irreducible subspaces changes smoothly when varying the value of ν. The formalism is of importance in physical theories which postulate analyticity requirements and Lorentz invariance simultaneously (e.g., Regge and Lorentz pole theory). In this paper we construct explicit basis functions of the representation spaces.

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

Pages (from-to) | 846-852 |

Number of pages | 7 |

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), 846-852.

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 12, no. 5, pp. 846-852.

}

TY - JOUR

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

AU - Szegö, K.

AU - Tóth, K.

PY - 1971

Y1 - 1971

N2 - Unitary and nonunitary representations of the SL(2, C) group are investigated in such a basis, in which the subgroup diagonalized is that one which in the four-dimensional representation leaves invariant the 4-vector pμ = (1/2(1 + ν), 0, 0, 1/2(1 - ν)) for an arbitrary real value of pμ 2 = ν. The split of the representation space into irreducible subspaces changes smoothly when varying the value of ν. The formalism is of importance in physical theories which postulate analyticity requirements and Lorentz invariance simultaneously (e.g., Regge and Lorentz pole theory). In this paper we construct explicit basis functions of the representation spaces.

AB - Unitary and nonunitary representations of the SL(2, C) group are investigated in such a basis, in which the subgroup diagonalized is that one which in the four-dimensional representation leaves invariant the 4-vector pμ = (1/2(1 + ν), 0, 0, 1/2(1 - ν)) for an arbitrary real value of pμ 2 = ν. The split of the representation space into irreducible subspaces changes smoothly when varying the value of ν. The formalism is of importance in physical theories which postulate analyticity requirements and Lorentz invariance simultaneously (e.g., Regge and Lorentz pole theory). In this paper we construct explicit basis functions of the representation spaces.

UR - http://www.scopus.com/inward/record.url?scp=36849097812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849097812&partnerID=8YFLogxK

M3 - Article

VL - 12

SP - 846

EP - 852

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 5

ER -