Fermionic realisations of simple Lie algebras and their invariant fermionic operators

Nuclear Physics B

Volumn 581, Issue 3, 2000, Pages 743-760

  De Azcarraga J A ^a   MacFarlane, A J ^b  

^a INSTITUTO DE FÍSICA CORPUSCULAR IFIC   (Spain)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

02.20. a; 02.40. k; 03.65.Fd; 11.30.Pb

Indexed keywords

EID: 0039671908     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(00)00236-4     Document Type: Article

References (23)

1. Brink L., Ramond P. Dirac equations, light cone supersymmetry and superconformal algebras. hep-th/9908208 . Contributed article to: M. Shifman (Ed.), Gelfand's Memorial Volume, World Scientific.
2. Treiman S.B., Jackiw R., Zumino B., Witten E. Current Algebra and Anomalies. 1985;World Scientific, Singapore.
3. de Azcárraga J.A., Izquierdo J.M. Lie groups, Lie Algebras, Cohomology and Some Applications in Physics. 1995;Cambridge Univ. Press, Cambridge, UK.
4. Faddeev L.D., Shatashvili S.L. Algebraic and hamiltonian methods in the theory of non-abelian anomalies. Theor. Math. Phys. Vol. 60:1984;770-778. (Teor. Mat. Fiz. 50 (1984) 206-217).
5. de Azcárraga J.A., Izquierdo J.M., Macfarlane A.J. Current algebra and Wess-Zumino terms: a unified geometric treatment. Ann. Phys. Vol. 202:1990;1-21.
6. d'Hoker E., Weinberg S. General effective actions. Phys. Rev. D. Vol. 50:1994;R6050-R6054.
7. d'Hoker E. Invariant effective actions, cohomology of homogeneous spaces and anomalies. Nucl. Phys. B. Vol. 451:1995;725-748.
8. de Azcárraga J.A., Macfarlane A.J., Perez Bueno J.C. Effective actions, relative cohomology and Chern-Simons terms. Phys. Lett. B. Vol. 419:1998;186-194.
9. Bergshoeff E., Bilal A., Stelle K. W -symmetries: gauging and symmetry. Mod. Phys. Lett. A. Vol. 6:1991;4959-4984.
10. Bouwknegt P., Schoutens K. W symmetry in conformal field theory. Phys. Rep. Vol. 223:1993;183-276.
11. Evans J.M., Hassan M., MacKay N.J., Mountain A.J. Local conserved charges and principal chiral models. Nucl. Phys. Vol. 561:1999;385-412.
12. de Azcárraga J.A., Macfarlane A.J., Mountain A.J., Pérez Bueno J.C. Invariant tensors for simple groups. Nucl. Phys. B. Vol. 510:1998;657-687.
13. Davis A.C., Macfarlane A.J., Gracey J.A. Anomalous current algebras in the Skyrme model and in chiral G×G with Wess-Zumino term. Phys. Lett. B. Vol. 194:1987;415-419.
14. Kostant B. A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups. Duke Math. J. Vol. 100:1999;447-501.
15. de Jonghe F., Macfarlane A.J., Peeters K., van Holten J.W. New symmetries of the monopole. Phys. Lett. B. Vol. 359:1995;114-117.
16. Tanimoto M. The role of Killing-Yano tensors in supersymmetric quantum mechanics on a curved manifold. Nucl. Phys. B. Vol. 442:1995;549-559.
17. Macfarlane A.J., Mountain A.J. Hidden supersymmetries of particle motion in a Wu-Yang monopole field. Phys. Lett. B. Vol. 373:1996;125-129.
18. Martin J.L. Generalized classical dynamics, and the "classical analogue" of a Fermi oscillator. Proc. R. Soc. (London). Vol. 251:1959;536-542.
19. Martin J.L. The Feynman principle for a Fermi system. Proc. R. Soc. (London). Vol. 251:1959;542-559.
20. Slansky R. Group theory for unified model building. Phys. Rep. Vol. 79:1981;1-128.
21. Fuchs J., Schwiegert C. Symmetries, Lie Algebras and Representations. 1997;Cambridge Univ. Press, Cambridge, UK.
22. Macfarlane A.J., Majid S.H. Quantum group structure in a fermionic extension of the quantum harmonic oscillator. Phys. Lett. B. Vol. 268:1991;71-74.
23. N symmetry and its applications. Ann. Phys. (N.Y.). Vol. 101:1976;394-412.