Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 056, 23 pages      hep-th/0510268      http://dx.doi.org/10.3842/SIGMA.2006.056

Extension of the Poincaré Symmetry and Its Field Theoretical Implementation

Adrian Tanasa
Laboratoire MIA, Faculté de Sciences et Techniques, Université de Haute Alsace, 4 rue des Frères Lumière, 68093 Mulhouse Cedex, France

Received October 31, 2005, in final form April 28, 2006; Published online May 29, 2006

Abstract
We define a new algebraic extension of the Poincaré symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding degrees of freedom, compatibility with Abelian gauge invariance etc. are done. Finally we analyse the possibilities of interaction terms for this model.

Key words: extensions of the Poincaré algebra; field theory; algebraic methods; Lie (super)algebras; gauge symmetry.

pdf (339 kb)   ps (224 kb)   tex (31 kb)

References

  1. O'Raifeartaigh L., Mass differences and Lie algebras of finite order, Phys. Rev. Lett., 1965, V.14, 575-577.
  2. Coleman S., Mandula J., All possible symmetries of the S matrix, Phys. Rev., 1967, V.159, 1251-1256.
  3. Lopuszanski J., An introduction to symmetry and supersymmetry in quantum field theory, Singapore, World Scientific Publishing, 1991.
  4. Streater R.F., Wightman A.S., PCT, spin and statistics and all that, New York, W.A. Benjamin, Inc., 1964.
  5. Haag R., Lopuszanski J.T., Sohnius M.F., All possible generators of supersymmetries of the S matrix, Nucl. Phys. B, 1976, V.88, 257-274.
  6. Rausch de Traubenberg M., Slupinski M.J., Finite-dimensional Lie algebras of order F, J. Math. Phys., 2002, V.43, 5145-5160, hep-th/0205113.
  7. Rausch de Traubenberg M., Slupinski M.J., Fractional supersymmetry and F(th) roots of representations, J. Math. Phys., 2000, V.41, 4556-4571, hep-th/9904126.
  8. Mohammedi N., Moultaka G., Rausch de Traubenberg M., Field theoretic realizations for cubic supersymmetry, Internat. J. Modern Phys. A, 2004, V.19, 5585-5608, hep-th/0305172.
  9. Moultaka G., Rausch de Traubenberg M., Tanasa A., Cubic supersymmetry and Abelian gauge invariance, Internat. J. Modern Phys. A, 2005, V.20, 5779-5806, hep-th/0411198.
  10. Beckers J., Debergh N., On parasupersymmetric coherent states, Modern Phys. Lett. A, 1989, V.4, 1209-1215.
  11. Beckers J., Debergh N., Poincaré invariance and quantum parasuperfields, Internat. J. Modern Phys. A, 1993, V.8, 5041-5061.
  12. Rubakov V.A., Spiridonov V.P., Parasupersymmetric quantum mechanics, Modern Phys. Lett. A, 1988, V.3, 1337-1347.
  13. Matheus-Valle J.L., Monteiro M.A.R., Quantum group generalization of the classical supersymmetric point particle, Modern Phys. Lett. A, 1992, V.7, 3023-3028.
  14. Durand S., Extended fractional supersymmetric quantum mechanics, Modern Phys. Lett. A, 1993, V.8, 1795-1804, hep-th/9305130.
  15. de Azcàrraga J.A., Macfarlane A.J., Group theoretical foundations of fractional supersymmetry, J. Math. Phys., 1996, V.37, 1115-1127, hep-th/9506177.
  16. Fleury N., Rausch de Traubenberg M., Local fractional supersymmetry for alternative statistics, Modern Phys. Lett. A, 1996, V.11, 899-914, hep-th/9510108.
  17. Dunne R.S., Macfarlane A.J., de Azcarraga J.A., Perez Bueno J.C., Geometrical foundations of fractional supersymmetry, Internat. J. Modern Phys. A, 1997, V.12, 3275-3306, hep-th/9610087.
  18. Perez A., Rausch de Traubenberg M., Simon P., 2D fractional supersymmetry for rational conformal field theory. Application for third-integer spin states, Nucl. Phys. B, 1996, V.482, 325-344, hep-th/9603149.
  19. Rausch de Traubenberg M., Simon P., 2-D fractional supersymmetry and conformal field theory for alternative statistics, Nucl. Phys. B, 1998, V.517, 485-505, hep-th/9606188.
  20. Rausch de Traubenberg M., Slupinski M.J., Non-trivial extensions of the 3D-Poincaré algebra and fractional supersymmetry for anyons, Modern Phys. Lett. A, 1997, V.12, 3051-3066, hep-th/9609203.
  21. Kerner R., Z(3) graded algebras and the cubic root of the supersymmetry translations, J. Math. Phys., 1992, V.33, 403-411.
  22. Filippov V.T., n-Lie algebras, Sibirsk. Mat. Zh., 1985, V.26, 126-140.
  23. Tanasa A., Lie subalgebras of the Weyl algebra. Lie algebras of order 3 and their application to cubic supersymmetry, hep-th/0509174.
  24. Goze M., Rausch de Traubenberg M., Tanasa A., Deformations, contractions and classifications of Lie algebras of order 3, math-ph/0603008.
  25. Sohnius M.F., Introducing supersymmetry, Phys. Rep., 1985, V.128, 39-204.
  26. Grignani G., Plyushchay M., Sodano P., A pseudoclassical model for P,T-invariant planar fermions, Nucl. Phys. B, 1996, V.464, 189-212, hep-th/9511072.
  27. Nirov K.S., Plyushchay M.S., P,T-invariant system of Chern-Simons fields: pseudoclassical model and hidden symmetries, Nucl. Phys. B, 1998, V.512, 295-319, hep-th/9803221.
  28. Plyushchay M.S., Hidden nonlinear supersymmetries in pure parabosonic systems, Internat. J. Modern Phys. A, 2000, V.15, 3679-3698, hep-th/9903130.
  29. Plyushchay M.S., Rausch de Traubenberg M., Cubic root of Klein-Gordon equation, Phys. Lett. B, 2000, V.477, 276-284, hep-th/0001067.
  30. Witten E., Lecture notes on supersymmetry, in Proc. Inter. School of Subnuclear Physics (Erice, 1981), Editor A. Zichichi, Plenum Press, 1983, 1-64.
  31. Polchinski J., String theory, Cambridge University Press, 2000.
  32. Gomis J., Paris J., Samuel S., Antibracket, antifields and gauge-theory quantization, Phys. Rep., 1995, V.259, 1-145, hep-th/9412228.
  33. Peskin M., Schroeder D., An introduction to quantum field theory, Perseus Books, 1980
  34. Horowitz G.T., Exactly soluble diffeomorphism invariant theories, Comm. Math. Phys., 1989, V.125, 417-437.
  35. Horowitz G.T., Srednicki M., A quantum field theoretic description of linking numbers and their generalization, Comm. Math. Phys., 1990, V.130, 83-94.
  36. Blau M., Thompson G., Topological gauge theories of antisymmetric tensor fields, Ann. Phys., 1991, V.205, 130-172.
  37. Blau M., Thompson G., Do metric independent classical actions lead to topological field theories?, Phys. Lett. B, 1991, V.255, 535-542.
  38. Rausch de Traubenberg M., Four dimensional cubic supersymmetry, hep-th/0312066.
  39. Moultaka G., Rausch de Traubenberg M., Tanasa A., Non-trivial extension of the Poincaré algebra for antisymmetric gauge fields, Contribution to the XI-th International Conference "Symmetry Methods in Physics" (June 21-24, 2004, Prague), hep-th/0407168.
  40. Henneaux M., Knaepen B., All consistent interactions for exterior form gauge fields, Phys. Rev. D, 1997, V.56, 6076-6080, hep-th/9706119.

Previous article   Next article   Contents of Volume 2 (2006)