An Alternative Approach to Generate Maxwell Algebras
Year 2018,
Volume: 14 Issue: 1, 23 - 31, 30.04.2018
Salih Kibaroğlu
,
Mustafa Şenay
,
Mustafa Aslan
Abstract
We present an alternative
method to produce Maxwell algebras. We show that D = 4 Maxwell algebras can be obtained by inducing
from D = 6 Maxwell-Lorentz algebra. From this method, some
Maxwell algebras are constructed.
References
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- Concha, P.K., Rodríguez, E.K. (2014) "N=1 Supergravity and Maxwell superalgebras", JHEP, vol. 1409, pp. 090.
- Durka, R., Kowalski-Glikman, J., Szczachor, M. (2012) "AdS-Maxwell superalgebra and supergravity", Mod.Phys.Lett. A, vol. 27, pp. 1250023.
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- Fedoruk, S., Lukierski, J. (2013) "New spinorial particle model in tensorial space-time and interacting higher spin fields", JHEP, vol. 1302, pp. 128.
- Castellani L., Perotto A., (1996) “Free Differential Algebras: Their Use in Field Theory and Dual Formulation”, Lett. Math. Phys., vol. 38, pp. 321.
- Hatsuda M., Sakaguchi M., (2003) “Wess-Zumino Term for The AdS Superstring and Generalized Inonu-Wigner Contraction”, Prog. Theor. Phys., vol. 109, pp. 853.
- de Azcárraga J. A., Izquierdo J. M., Picon M., Varela O., (2003) “Generating Lie and Gauge Free Differential (Super)Algebras by Expanding Maurer–Cartan Forms and Chern–Simons Supergravity”, Nucl. Phys. B, vol. 662, pp. 185.
- de Azcárraga J. A., Izquierdo J. M., Picon M., Varela O., (2004) “Extension, Expansion, Lie Algebra Cohomology and Enlarged Superspace”, Class. Quantum Grav., vol. 21, pp. 1375.
- de Azcárraga J. A., Izquierdo J. M., Picon M., Varela O., (2007) “Expansion of Algebras and Superalgebras and Some Applications”, Class. Quantum Grav. Int. J. Theor. Phys., 2007, vol. 46, pp. 2738.
- de Azcárraga J. A., Izquierdo J. M., Lukierski J., Woronowicz M., (2013) “Generalizations of Maxwell (Super)Algebras by The Expansion Method”, Nucl. Phys. B, vol. 869, pp. 303–314.
- Gibbons G. W., Gomis J., Pope C. N., (2007) “General Very Special Relativity is Finsler Geometry”, Phys. Rev. D, DOI: 10.1103/PhysRevD.76.081701.
- Izaurieta F., Rodriguez E., Salgado P., (2006) “Expanding Lie (Super)Algebras Through Abelian Semigroups”, J. Math. Phys., DOI: 10.1063/1.2390659.
- Diaz J., Fierro O., Izaurieta F., Merino N., Rodriguez E., Salgado P., Valdivia O., (2012) “A Generalized Action for (2+1)-Dimensional Chern-Simons Gravity”, J. Phys. A: Math. Theor., DOI: 10.1088/1751-8113/45/25/255207.
- de Azcárraga J. A., Izquierdo J. M., “Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics”, 1st Ed, Cambridge University Press, Cambridge, 1995.
- Bonanos S., Gomis J., (2008) “A Note on The Chevalley–Eilenberg Cohomology for The Galilei and Poincare Algebras”, J. Phys. A, DOI: 10.1088/1751-8113/42/14/145206.
- Bonanos S., Gomis J., (2008) “Infinite Sequence of Poincare Group Extensions: Structure and Dynamics”, J. Phys. A, DOI: 10.1088/1751-8113/43/1/015201.
Year 2018,
Volume: 14 Issue: 1, 23 - 31, 30.04.2018
Salih Kibaroğlu
,
Mustafa Şenay
,
Mustafa Aslan
References
- Schrader, R. (1972) "The Maxwell Group and the Quantum Theory of Particles in Classical Homogeneous Electromagnetic Fields", Fortschritte der Physik, vol. 20, pp. 701-734.
- Bacry, H., Combe, P., Richard, J. L., (1970) "Group-theoretical analysis of elementary particles in an external electromagnetic field II. The nonrelativistic particle in a constant and uniform field", Il Nuovo Cimento, vol. 70, pp. 289-312.
- Bacry, H., Combe, P., Richard, J. L., (1970) "Group-theoretical analysis of elementary particles in an external electromagnetic field", Il Nuovo Cimento, vol. 67, pp. 267-299.
- Beckers, J., Hussin, V. (1983) "Minimal electromagnetic coupling schemes. II. Relativistic and nonrelativistic Maxwell groups", J. Math. Phys., vol. 24, pp. 1295.
- Negro, J., del Olmo, M. A. (1990) "Local realizations of kinematical groups with a constant electromagnetic field. I. The relativistic case", J. Math. Phys., vol. 31, pp. 568.
- Negro, J., del Olmo, M. A. (1990) "Local realizations of kinematical groups with a constant electromagnetic field. II. The nonrelativistic case", J. Math. Phys., 31, pp. 2811.
- Soroka, D.V., Soroka, V.A. (2005) "Tensor extension of the Poincare' algebra", Phys.Lett. B, vol. 607, pp. 302-305.
- Bonanos, S., Gomis, J. (2009) "A note on the Chevalley–Eilenberg cohomology for the Galilei and Poincaré algebras", J. Phys. A, vol. 42, pp. 145206.
- Bonanos, S., Gomis, J. (2010) "Infinite Sequence of Poincare Group Extensions: Structure and Dynamics", J. Phys. A, vol. 43, pp. 015201.
- Gibbons, G.W., Gomis, J., Pope, C.N. (2010) "Deforming the Maxwell-Sim Algebra", Phys. Rev. D, vol. 82, pp. 065002.
- Gomis, J., Kamimura, K., Lukierski, J. (2009) "Deformations of Maxwell algebra and their Dynamical Realizations", JHEP, vol. 08, pp. 39.
- Salgado, P., Salgado S. (2013) "so(D−1,1)⊕so(D−1,2) algebras and gravity", Physics Letters B, vol. 728, pp. 5-10.
- de Azcárraga, J.A., Kamimura, K., Lukierski, J. (2011) "Generalized cosmological term from Maxwell symmetries", Phys.Rev. D, vol. 83, pp. 124036.
- de Azcárraga, J.A., Kamimura, K., Lukierski, J. (2013) "Maxwell symmetries and some applications", Int.J.Mod.Phys.Conf.Ser., vol. 23, pp. 01160.
- Cebecioğlu, O., Kibaroğlu, S. (2014) "Gauge theory of the Maxwell-Weyl group", Phys. Rev. D, vol. 90, pp. 084053.
- Cebecioğlu, O., Kibaroğlu, S. (2015) "Maxwell-Affine gauge theory of gravity", Phys. Lett. B, vol. 751, pp. 131-134.
- Durka, R., Kowalski-Glikman, J., Szczachor, M. (2011) "Gauged AdS-Maxwell algebra and gravity", Mod.Phys.Lett. A, vol. 26, pp. 2689- 2696.
- Hoseinzadeh, S., Rezaei-Aghdam, A. (2014) "(2+1)-dimensional gravity from Maxwell and semisimple extension of the Poincaré gauge symmetric models", Phys. Rev. D, vol. 90, pp. 084008.
- Inostroza, C., Salazar, A., Salgado, P. (2014) "Brans–Dicke gravity theory from topological gravity", Phys.Lett. B, vol. 734, pp. 377–382.
- Salgado, S., Izaurieta, F., González, N., Rubio, G. (2014) "Gauged Wess–Zumino–Witten actions for generalized Poincaré algebras", Physics Letters B, vol. 732, pp. 255-262.
- Soroka, D.V., Soroka, V.A. (2012) "Gauge semi-simple extension of the Poincar´e group", Phys.Lett. B, vol. 707, pp. 160-162.
- de Azcárraga, J. A., Izquierdo, J. M. (2014) "Minimal D=4 supergravity from the superMaxwell algebra", Nuclear Physics B, vol. 885, pp. 34–45.
- Bonanos, S., Gomis, J., Kamimura, K., Lukierski, J. (2010) "Maxwell Superalgebra and Superparticles in Constant Gauge Backgrounds", Phys. Rev. Lett., vol. 104, pp. 090401.
- Concha, P.K., Rodríguez, E.K. (2014) "N=1 Supergravity and Maxwell superalgebras", JHEP, vol. 1409, pp. 090.
- Durka, R., Kowalski-Glikman, J., Szczachor, M. (2012) "AdS-Maxwell superalgebra and supergravity", Mod.Phys.Lett. A, vol. 27, pp. 1250023.
- Fedoruk, S., Lukierski, J. (2012) "New particle model in extended space-time and covariantization of planar Landau dynamics", Phys.Lett. B, vol. 718, pp. 646-652.
- Fedoruk, S., Lukierski, J. (2013) "Maxwell group and HS field theory", J. Phys. Conf. Ser., vol. 474, pp. 012016.
- Fedoruk, S., Lukierski, J. (2013) "New spinorial particle model in tensorial space-time and interacting higher spin fields", JHEP, vol. 1302, pp. 128.
- Castellani L., Perotto A., (1996) “Free Differential Algebras: Their Use in Field Theory and Dual Formulation”, Lett. Math. Phys., vol. 38, pp. 321.
- Hatsuda M., Sakaguchi M., (2003) “Wess-Zumino Term for The AdS Superstring and Generalized Inonu-Wigner Contraction”, Prog. Theor. Phys., vol. 109, pp. 853.
- de Azcárraga J. A., Izquierdo J. M., Picon M., Varela O., (2003) “Generating Lie and Gauge Free Differential (Super)Algebras by Expanding Maurer–Cartan Forms and Chern–Simons Supergravity”, Nucl. Phys. B, vol. 662, pp. 185.
- de Azcárraga J. A., Izquierdo J. M., Picon M., Varela O., (2004) “Extension, Expansion, Lie Algebra Cohomology and Enlarged Superspace”, Class. Quantum Grav., vol. 21, pp. 1375.
- de Azcárraga J. A., Izquierdo J. M., Picon M., Varela O., (2007) “Expansion of Algebras and Superalgebras and Some Applications”, Class. Quantum Grav. Int. J. Theor. Phys., 2007, vol. 46, pp. 2738.
- de Azcárraga J. A., Izquierdo J. M., Lukierski J., Woronowicz M., (2013) “Generalizations of Maxwell (Super)Algebras by The Expansion Method”, Nucl. Phys. B, vol. 869, pp. 303–314.
- Gibbons G. W., Gomis J., Pope C. N., (2007) “General Very Special Relativity is Finsler Geometry”, Phys. Rev. D, DOI: 10.1103/PhysRevD.76.081701.
- Izaurieta F., Rodriguez E., Salgado P., (2006) “Expanding Lie (Super)Algebras Through Abelian Semigroups”, J. Math. Phys., DOI: 10.1063/1.2390659.
- Diaz J., Fierro O., Izaurieta F., Merino N., Rodriguez E., Salgado P., Valdivia O., (2012) “A Generalized Action for (2+1)-Dimensional Chern-Simons Gravity”, J. Phys. A: Math. Theor., DOI: 10.1088/1751-8113/45/25/255207.
- de Azcárraga J. A., Izquierdo J. M., “Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics”, 1st Ed, Cambridge University Press, Cambridge, 1995.
- Bonanos S., Gomis J., (2008) “A Note on The Chevalley–Eilenberg Cohomology for The Galilei and Poincare Algebras”, J. Phys. A, DOI: 10.1088/1751-8113/42/14/145206.
- Bonanos S., Gomis J., (2008) “Infinite Sequence of Poincare Group Extensions: Structure and Dynamics”, J. Phys. A, DOI: 10.1088/1751-8113/43/1/015201.