Unitary Irreducible Representations of SU(2, 2). III. Reduction with Respect to an Iso-Poincaré Subgroup
- Univ. of Pittsburgh, PA (United States)
The unitary irreducible representations of SU(2, 2), the covering group of the conformal group, are reduced with respect to an iso-Poincaré subgroup E(3, 1). Explicit representations of the 15 generators of SU(2, 2) in terms of differential operators in the function space of |η,ξ,ε;s,t,m$$\rangle$$, |ω,ξ,ε;r,t,m$$\rangle$$, and |ξ,ε;t,m$$\rangle$$, the basis vectors for "timelike,'' "spacelike,'' and "lightlike'' UIR's of E(3, 1), respectively, are given. The matrix elements between a basis vector in the maximal compact subgroup SU(2) × SU(2) × U(1) and a basis vector in E(3, 1) are calculated for all 14 different classes of UIR's of SU(2, 2). He we find that two classes are reducible with respect to "lightlike'' representations, two classes are reducible with respect to "timelike'' representations, eight classes are reducible with respect to ``spacelike'' representations, and two classes contain both "timelike'' and "spacelike'' representations of E(3, 1).
- Research Organization:
- Univ. of Pittsburgh, PA (United States)
- Sponsoring Organization:
- US Atomic Energy Commission (AEC)
- NSA Number:
- NSA-24-045555
- OSTI ID:
- 4101369
- Alternate ID(s):
- OSTI ID: 4007967
- Report Number(s):
- NYO--3829-52
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 12; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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