The Two-Component Majorana Equation-Novel Derivations and Known Symmetries ()
Abstract
We revisit the two-component Majorana equation and derive it in a new form by linearizing the relativistic dispersion relation of a massive particle, in a way similar to that used to derive the Dirac equation. We are using thereby the Pauli spin matrices, corresponding to an irreducible representation of the Lorentz group, and a lucid and transparent algebraic approach exploiting the newly introduced spin-flip operator. Thus we can readily build up the Majorana version of the Dirac equation in its chiral representation. The Lorentz-invariant complex conjugation operation involves the spin-flip operator, and its connection to chiral symmetry is discussed. The eigenfunctions of the Majorana equation are calculated in a concise way.
Share and Cite:
E. Marsch, "The Two-Component Majorana Equation-Novel Derivations and Known Symmetries,"
Journal of Modern Physics, Vol. 2 No. 10, 2011, pp. 1109-1114. doi:
10.4236/jmp.2011.210137.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
E. Majorana, “Teoria Simmetrica Dell’ Elettrone E Del Positrone,” Il Nuovo Cimento (1924-1942), Vol. 14, No. 4, 1937, pp. 171-184. doi:10.1007/BF02961314
|
|
[2]
|
R. N. Mohapatra and P. B. Pal, “Massive Neutrinos in Physics and Astrophysics,” World Scientific, Singapore, 2004. doi:10.1142/9789812562203
|
|
[3]
|
M. Fukugita and T. Yanagida, “Physics of Neutrinos and Applications to Astrophysics,” Springer, Berlin, 2003.
|
|
[4]
|
M. Kaku, “Quantum Field Theory, A Modern Introduction,” Oxford University Press, New York, 1993.
|
|
[5]
|
H. Weyl, “Elektron und Gravitation I,” Zeitschrift für Physik A Hadrons and Nuclei, Vol. 56, No. 5-6, 1929, pp. 330-352. doi:10.1007/BF01339504
|
|
[6]
|
W. Pauli, “Zur Quantenmechanik des Magnetischen Elektrons,” Zeitschrift für Physik A Hadrons and Nuclei, Vol. 43, No. 9-10, 1927, pp. 601-623.
doi:10.1007/BF01397326
|
|
[7]
|
P. B. Pal, “Dirac, Majorana and Weyl Fermions,” arXiv:1006.1718v2 [hep-ph], 2010.
|
|
[8]
|
P. M. A. Dirac, “The Quantum Theory of the Electron,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 117, No. 778, 1928, pp. 610-624.
|
|
[9]
|
A. Das, “Lectures on Quantum Field Theory,” World Scientific, Singapore, 2008.
doi:10.1142/9789812832870
|