Abstract
We propose a new constructive scheme for real SuSy algebras within the general formalism of real Clifford algebra theory, and use it to characterize a natural holomorphic extension admitted by a subclass of real SuSy algebras in signaturess−t=3 mod 4. The resulting holomorphic SuSy algebras are the abstract models of a new type of supersymmetry algebras, already known to be relevant in the development of canonical or Hamiltonian methods in superspace.
Similar content being viewed by others
References
J. Lukierski, “Euclidean Superalgebras for 3 ≤D ≤ 10,” in Proceedings, 1985 Nuffield Workshop, Cambridge:Supersymmetry and its Applications, G. W. Gibbons, S. W. Hawking, and P. K. Townsend, eds. (Cambridge University Press, Cambridge, 1986). J. Lukierski, “Holomorphic and real Euclidean supersymmetries in three and four dimensions,” ICTP preprint IC/86/292, Trieste, 1986.
R. A. Marques Pereira,Class Quantum Grav. 4, 411 (1987).
M. F. Atiyah, R. Bott, and A. Shapiro,Topology 3, Suppl. 1, 3 (1964). M. Marcus,Finite-Dimensional Multilinear Algebra, Parts 1 and 2 (Marcel Dekker, New York, 1973, 1975). D. Husemoller,Fibre Bundles, 2nd edn. (Springer, New York, 1975). I. R. Porteous,Topological Geometry, 2nd edn. (Cambridge University Press, Cambridge, 1981). P. Lounesto,Found. Phys. 11, 721 (1981). H. B. Lawson Jr. and M. L. Michelsohn,Spin Geometry (Universidade Federal do Ceará and IMPA Press, Fortaleza, Brazil, 1983). P. Lounesto, in Proceedings, 1985 NATO and SERC Workshop, Canterbury:Clifford Algebras and their Applications in Mathematical Physics, J. S. R. Chisholm and A. K. Common, eds. (Reidel, Dordrecht, 1986). R. Coquereaux, “Spinors, reflections and clifford algebras: A review,” University of Texas at Austin preprint UTTG-21-85, Austin, 1985; to appear inSpinors in Physics and Geometry, Furlan and Trautman, eds. (World Scientific, Singapore, 1988).
Z. Hasiewicz, A. K. Kwasniewski, and P. Morawiec,J. Math. Phys. 25, 2031 (1984).
V. G. Kac,Commun. Math. Phys. 53, 31 (1977).
R. A. Marques Pereira, Centre de Physique Théorique preprint CPT-88/P.2149, Marseille, 1988.
Author information
Authors and Affiliations
Additional information
Research supported in part by CNPq-Brazil.
Rights and permissions
About this article
Cite this article
Marques Pereira, R.A. Real and holomorphic SuSy algebras. Found Phys 19, 755–782 (1989). https://doi.org/10.1007/BF00731911
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00731911