Generalized supersymmetry and Lévy-Leblond equation

N. Aizawa, Z. Kuznetsova, H. Tanaka, F. Toppan

Resumo


The symmetries of the L\'evy-Leblond equation are investigated beyond the standard Lie framework.
It is shown that the equation has two remarkable symmetries.
One is given by the super Schr\"odinger algebra and the other is by a $\ZZ$ graded Lie algebra.
The $\ZZ$ graded Lie algebra is achieved by transforming bosonic into fermionic operators in the super Schr\"odinger algebra
and introducing second order differential operators as generators of symmetry.

Texto completo:

PDF

Referências


N. Aizawa, Z. Kuznetsova, H. Tanaka, F. Toppan, {textit{$ZZ$-graded Lie Symmetries of the L'evy-Leblond Equations}}, preprint CBPF-NF-004/16.

C. P. Boyer, Helv. Phys. Acta, textbf{47} (1974) 589

C. Duval and P. A. Horv'athy, J. Math. Phys. textbf{35} (1994) 2516

W. Fushchych, R. Zhdanov,

textit{Symmetries and Exact Solutions of Nonlinear Dirac Equations}, (Mathematical Ukraina Publisher, 1997)

J. P. Gauntlett, J. Gomis, P. K. Townsend,

Phys. Lett. textbf{B248} (1990) 288

P. A. Horv'athy,

textit{Non-relativistic conformal and supersymmetries},

arXiv:0807.0513 [hep-th]

P. A. Horv'athy, M. S. Plyushchay and M. Valenzuela,

J. Math. Phys. textbf{51} (2010) 092108

P. D. Jarvis, M. Yang and B. G. Wybourne, J. Math. Phys. textbf{28} (1987) 1192

J.-M. L'evy-Leblond, Comm. Math. Phys. textbf{6} (1967) 286

J. Lukierski, V. Rittenberg, Phys. Rev. textbf{D18} (1978) 385

U. Niederer, Helv. Phys. Acta, textbf{47} (1974) 167

V. Rittenberg, D. Wyler, Nucl. Phys. textbf{B139} (1978) 189

V. Rittenberg, D. Wyler, J. Math. Phys. textbf{19} (1978) 2193

M. Scheunert, J. Math. Phys. textbf{20} (1979) 712

V. N. Tolstoy, Phys. Part. Nucl. Lett. textbf{11} (2014) 933

F. Toppan, J. Phys. Conf. Ser. textbf{597} (2015) 012071

M. A. Vasiliev, Class. Quantum Grav. textbf{2} (1985) 645

A. A. Zheltukhin, Teor. Mat. Fiz. textbf{71} (1987) 218


Apontamentos

  • Não há apontamentos.