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Extension of the Poincaré Symmetry and Its Field Theoretical Implementation
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: extensions of the Poincaré algebra; field theory; algebraic methods; Lie (super)-algebras; gauge symmetry. 
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Adrian Tanasa. Extension of the Poincaré Symmetry and Its Field Theoretical Implementation. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a55/

[1] O'Raifeartaigh L., “Mass differences and Lie algebras of finite order”, Phys. Rev. Lett., 14 (1965), 575–577 | DOI | MR

[2] Coleman S., Mandula J., “All possible symmetries of the $S$ matrix”, Phys. Rev., 159 (1967), 1251–1256 | DOI | Zbl

[3] Lopuszanski J., An introduction to symmetry and supersymmetry in quantum field theory, World Scientific Publishing, Singapore, 1991 | MR

[4] Streater R. F., Wightman A. S., PCT, spin and statistics and all that, W. A. Benjamin, Inc., New York, 1964 | MR | Zbl

[5] Haag R., Lopuszanski J. T., Sohnius M. F., “All possible generators of supersymmetries of the $S$ matrix”, Nucl. Phys. B, 88 (1976), 257–274 | DOI | MR

[6] Rausch de Traubenberg M., Slupinski M. J., “Finite-dimensional Lie algebras of order $F$”, J. Math. Phys., 43 (2002), 5145–5160 ; arXiv:hep-th/0205113 | DOI | MR | Zbl

[7] Rausch de Traubenberg M., Slupinski M. J., “Fractional supersymmetry and $F$(th) roots of representations”, J. Math. Phys., 41 (2000), 4556–4571 ; arXiv:hep-th/9904126 | DOI | MR | Zbl

[8] Mohammedi N., Moultaka G., Rausch de Traubenberg M., “Field theoretic realizations for cubic supersymmetry”, Internat. J. Modern Phys. A, 19 (2004), 5585–5608 ; arXiv:hep-th/0305172 | DOI | MR | Zbl

[9] Moultaka G., Rausch de Traubenberg M., Tanasa A., “Cubic supersymmetry and Abelian gauge invariance”, Internat. J. Modern Phys. A, 20 (2005), 5779–5806 ; arXiv:hep-th/0411198 | DOI | MR | Zbl

[10] Beckers J., Debergh N., “On parasupersymmetric coherent states”, Modern Phys. Lett. A, 4 (1989), 1209–1215 | DOI | MR

[11] Beckers J., Debergh N., “Poincaré invariance and quantum parasuperfields”, Internat. J. Modern Phys. A, 8 (1993), 5041–5061 | DOI | MR | Zbl

[12] Rubakov V. A., Spiridonov V. P., “Parasupersymmetric quantum mechanics”, Modern Phys. Lett. A, 3 (1988), 1337–1347 | DOI | MR

[13] Matheus-Valle J. L., Monteiro M. A. R., “Quantum group generalization of the classical supersymmetric point particle”, Modern Phys. Lett. A, 7 (1992), 3023–3028 | DOI | MR | Zbl

[14] Durand S., “Extended fractional supersymmetric quantum mechanics”, Modern Phys. Lett. A, 8 (1993), 1795–1804 ; arXiv:hep-th/9305130 | DOI | MR | Zbl

[15] de Azcàrraga J. A., Macfarlane A. J., “Group theoretical foundations of fractional supersymmetry”, J. Math. Phys., 37 (1996), 1115–1127 ; arXiv:hep-th/9506177 | DOI | MR | Zbl

[16] Fleury N., Rausch de Traubenberg M., “Local fractional supersymmetry for alternative statistics”, Modern Phys. Lett. A, 11 (1996), 899–914 ; arXiv:hep-th/9510108 | DOI | MR

[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, 12 (1997), 3275–3306 ; arXiv:hep-th/9610087 | DOI | MR

[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, 482 (1996), 325–344 ; arXiv:hep-th/9603149 | DOI | MR | Zbl

[19] Rausch de Traubenberg M., Simon P., “2-D fractional supersymmetry and conformal field theory for alternative statistics”, Nucl. Phys. B, 517 (1998), 485–505 ; arXiv:hep-th/9606188 | DOI | MR | Zbl

[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, 12 (1997), 3051–3066 ; arXiv:hep-th/9609203 | DOI | MR

[21] Kerner R., “$Z$(3) graded algebras and the cubic root of the supersymmetry translations”, J. Math. Phys., 33 (1992), 403–411 | DOI | MR

[22] Filippov V. T., “$n$-Lie algebras”, Sibirsk. Mat. Zh., 26 (1985), 126–140 | MR | Zbl

[23] Tanasa A., Lie subalgebras of the Weyl algebra. Lie algebras of order 3 and their application to cubic supersymmetry, arXiv:hep-th/0509174

[24] Goze M., Rausch de Traubenberg M., Tanasa A., Deformations, contractions and classifications of Lie algebras of order $3$, arXiv:math-ph/0603008

[25] Sohnius M.F., “Introducing supersymmetry”, Phys. Rep., 128 (1985), 39–204 | DOI | MR

[26] Grignani G., Plyushchay M., Sodano P., “A pseudoclassical model for $P,T$-invariant planar fermions”, Nucl. Phys. B, 464 (1996), 189–212 ; arXiv:hep-th/9511072 | DOI | MR | Zbl

[27] Nirov K. S., Plyushchay M. S., “$P,T$-invariant system of Chern–Simons fields: pseudoclassical model and hidden symmetries”, Nucl. Phys. B, 512 (1998), 295–319 ; arXiv:hep-th/9803221 | DOI | MR | Zbl

[28] Plyushchay M. S., “Hidden nonlinear supersymmetries in pure parabosonic systems”, Internat. J. Modern Phys. A, 15 (2000), 3679–3698 ; arXiv:hep-th/9903130 | MR | Zbl

[29] Plyushchay M. S., Rausch de Traubenberg M., “Cubic root of Klein–Gordon equation”, Phys. Lett. B, 477 (2000), 276–284 ; arXiv:hep-th/0001067 | DOI | MR | Zbl

[30] Witten E., “Lecture notes on supersymmetry”, Proc. Inter. School of Subnuclear Physics (Erice, 1981), ed. A. Zichichi, Plenum Press, 1983, 1–64 | MR

[31] Polchinski J., String theory, Cambridge University Press, 2000

[32] Gomis J., Paris J., Samuel S., “Antibracket, antifields and gauge-theory quantization”, Phys. Rep., 259 (1995), 1–145 ; arXiv:hep-th/9412228 | DOI | MR

[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., 125 (1989), 417–437 | DOI | MR | Zbl

[35] Horowitz G. T., Srednicki M., “A quantum field theoretic description of linking numbers and their generalization”, Comm. Math. Phys., 130 (1990), 83–94 | DOI | MR | Zbl

[36] Blau M., Thompson G., “Topological gauge theories of antisymmetric tensor fields”, Ann. Phys., 205 (1991), 130–172 | DOI | MR | Zbl

[37] Blau M., Thompson G., “Do metric independent classical actions lead to topological field theories?”, Phys. Lett. B, 255 (1991), 535–542 | DOI | MR

[38] Rausch de Traubenberg M., Four dimensional cubic supersymmetry, arXiv: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)

[40] Henneaux M., “All consistent interactions for exterior form gauge fields”, Phys. Rev. D, 56 (1997), 6076–6080 ; arXiv:hep-th/9706119 | DOI | MR