×
Bracken, A. J.; Cant, A.

Singular indecomposable representations of sl(2,\({\mathbb{C}})\) and relativistic wave equations. (English) Zbl 0693.22007

J. Math. Phys. 30, No. 12, 2963-2972 (1989).
Singular indecomposable representations of the algebra \({\mathfrak s}{\mathfrak l}(2,C)\) are constructed (in the terminology of Gel’fand and Ponomarev). These admit vector operators \(\Gamma_{\mu}\) acting on the direct sum of such indecomposable representations. Hence invariant wave equations of the type \((\Gamma_{\mu}\partial^{\mu}+i K)\psi =0\) can be considered.
Reviewer: A.O.Barut

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
35Q99 Partial differential equations of mathematical physics and other areas of application

Keywords:

indecomposable representations; invariant wave equations
Cite Review PDF
Full Text: DOI Link

References:

[1] Gel’fand I. M., Zh. Eksp. Teor. Fiz. 18 pp 703– (1948)
[2] DOI: 10.1016/S0031-8914(42)90113-7 · Zbl 0060.45108 · doi:10.1016/S0031-8914(42)90113-7
[3] DOI: 10.1016/S0031-8914(42)90113-7 · Zbl 0060.45108 · doi:10.1016/S0031-8914(42)90113-7
[4] DOI: 10.1103/PhysRev.71.793 · Zbl 0032.37202 · doi:10.1103/PhysRev.71.793
[5] DOI: 10.1017/S1446181100001802 · Zbl 0396.17011 · doi:10.1017/S1446181100001802
[6] Bauer F. L., Sitzb. Bayer. Akad. Wiss 13 pp 111– (1952)
[7] DOI: 10.1063/1.1666214 · doi:10.1063/1.1666214
[8] DOI: 10.1088/0305-4470/8/5/015 · doi:10.1088/0305-4470/8/5/015
[9] DOI: 10.1063/1.525374 · doi:10.1063/1.525374
[10] DOI: 10.1063/1.524953 · Zbl 0468.35059 · doi:10.1063/1.524953
[11] DOI: 10.1063/1.526646 · Zbl 0587.53020 · doi:10.1063/1.526646
[12] DOI: 10.1063/1.524005 · doi:10.1063/1.524005
[13] DOI: 10.1098/rspa.1945.0003 · Zbl 0061.25311 · doi:10.1098/rspa.1945.0003
[14] DOI: 10.1007/BF02214096 · doi:10.1007/BF02214096
[15] DOI: 10.1070/RM1968v023n02ABEH001237 · Zbl 0236.22012 · doi:10.1070/RM1968v023n02ABEH001237
[16] DOI: 10.1070/RM1968v023n02ABEH001237 · Zbl 0236.22012 · doi:10.1070/RM1968v023n02ABEH001237
[17] DOI: 10.1063/1.1665515 · Zbl 0226.22014 · doi:10.1063/1.1665515
[18] DOI: 10.1063/1.1665515 · Zbl 0226.22014 · doi:10.1063/1.1665515
[19] DOI: 10.1063/1.1665515 · Zbl 0226.22014 · doi:10.1063/1.1665515
[20] DOI: 10.1063/1.525124 · doi:10.1063/1.525124
[21] DOI: 10.1063/1.525124 · doi:10.1063/1.525124
[22] DOI: 10.1088/0305-4470/16/16/011 · Zbl 0535.22011 · doi:10.1088/0305-4470/16/16/011
[23] DOI: 10.1088/0305-4470/16/16/011 · Zbl 0535.22011 · doi:10.1088/0305-4470/16/16/011
[24] DOI: 10.1103/PhysRevD.10.1168 · doi:10.1103/PhysRevD.10.1168
[25] Bargmann V., Math. Rev. 10 pp 4– (1949)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.