Research PapersNo Access

Division algebra representations of SO(4, 2)

Joshua Kincaid

Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA

Search for more papers by this author

and

Tevian Dray

Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA

Search for more papers by this author

https://doi.org/10.1142/S0217732314501284Cited by:5 (Source: Crossref)

Abstract

Representations of SO(4, 2) are constructed using 4×4 and 2×2 matrices with elements in ℍ' ⊗ ℂ and the known isomorphism between the conformal group and SO(4, 2) is written explicitly in terms of the 4×4 representation. The Clifford algebra structure of SO(4, 2) is briefly discussed in this language, as is its relationship to other groups of physical interest.

Keywords:

PACS: 11.10.Kk, 11.30.Cp, 11.30.Ly

References

T. Kugo and P. Townsend , Nucl. Phys. B 221 , 357 ( 1983 ) . Crossref, Web of Science, ADS, Google Scholar
A. Sudbery , J. Phys. A 17 , 939 ( 1984 ) . Crossref, ADS, Google Scholar
K. W. Chung and A. Sudbery , Phys. Lett. B 198 , 161 ( 1987 ) . Crossref, Web of Science, ADS, Google Scholar
D. B. Fairlie and C. A. Manogue , Phys. Rev. D 34 , 1832 ( 1986 ) . Crossref, Web of Science, ADS, Google Scholar
D. B. Fairlie and C. A. Manogue , Phys. Rev. D 36 , 475 ( 1987 ) . Crossref, Web of Science, ADS, Google Scholar
C. A. Manogue and A. Sudbery , Phys. Rev. D 40 , 4073 ( 1989 ) . Crossref, Web of Science, ADS, Google Scholar
C. A. Manogue and J. Schray , J. Math. Phys. 34 , 3746 ( 1993 ) . Crossref, Web of Science, ADS, Google Scholar
C. A. Manogue and T. Dray , Mod. Phys. Lett. A 14 , 1243 ( 1999 ) . Link, Web of Science, ADS, Google Scholar
C. A. Manogue and T. Dray , Mod. Phys. Lett. A 14 , 99 ( 1999 ) . Link, Web of Science, ADS, Google Scholar
T. Dray and C. A. Manogue, Clifford Algebras and Mathematical Physics, eds. R. Abłamowicz and B. Fauser (Birkhäuser, 2000) pp. 29–46. Google Scholar
H. Freudenthal , Adv. Math. 1 , 145 ( 1964 ) . Crossref, Google Scholar
J. Tits , Indagat. Math. 28 , 223 ( 1966 ) . Crossref, Google Scholar
E. B. Vinberg , Trudy Sem. Vekt. Tenz. Anal. 13 , 7 ( 1966 ) . Google Scholar
C. H. Barton and A. Sudbery , Adv. Math. 180 , 596 ( 2003 ) . Crossref, Web of Science, Google Scholar
F. Gursey , P. Ramond and P. Sikivie , Phys. Lett. B 60 , 177 ( 1976 ) . Crossref, Web of Science, ADS, Google Scholar
D. J. Gross et al. , Phys. Rev. Lett. 54 , 502 ( 1985 ) . Crossref, Web of Science, ADS, Google Scholar
A. Trautman, Encyclopedia of Mathematical Physics 1, eds. J.-P. Françoise, G. L. Naber and T. S. Tsun (Elsevier, 2006) pp. 518–530. Crossref, Google Scholar
R. Penrose and W. Rindler , Spinors and Space-Time 2 ( Cambridge Univ. Press , 1986 ) . Crossref, Google Scholar
T. Dray, J. Huerta and J. Kincaid, The 2 × 2 Lie group magic square, in preparation . Google Scholar
J. J. Kincaid, Division algebra representations of SO(4, 2), Master's thesis, Oregon State University (2012), , http://ir.library.oregonstate.edu/xmlui/handle/1957/30682 . Google Scholar