Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

WANG Hai-Jun

doi:10.1088/1674-1137/33/6/016

Chinese Physics C> 2009, Vol. 33> Issue(6) : 487-493 DOI: 10.1088/1674-1137/33/6/016

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

WANG Hai-Jun ^,

Center for Theoretical Physics and School of Physics, Jilin University, Changchun 130023, China

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In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL(2,C) and the Lorentz group via the Pauli grading (the elements of SL(2,C) expressed by direct sum of unit matrix and generators of SU(2) group), we grade the SL(3,C) group with the generators of SU(3), i. e. the Gell-Mann matrices, then express the SU(3) group in terms of three SU(2) subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL(2,C). If the mapping from group SL(3,C) to the Lorentz group is constructed by choosing one SU(2) subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex γ_μ \vpartial^μ is extended to encompass γ₅γ_μ\vpartial^μ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.

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WANG Hai-Jun. Lorentz violation constrained by triplicity of lepton families and neutrino oscillations[J]. Chinese Physics C, 2009, 33(6): 487-493. doi: 10.1088/1674-1137/33/6/016

WANG Hai-Jun. Lorentz violation constrained by triplicity of lepton families and neutrino oscillations[J]. Chinese Physics C, 2009, 33(6): 487-493. doi: 10.1088/1674-1137/33/6/016 shu

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Received: 2008-07-24
Revised: 2008-08-28

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沈阳化工大学材料科学与工程学院沈阳 110142

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

Corresponding author: WANG Hai-Jun,

Center for Theoretical Physics and School of Physics, Jilin University, Changchun 130023, China

Received Date: 2008-07-24

Accepted Date: 2008-08-28

Available Online: 2009-06-05

Abstract: In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL(2,C) and the Lorentz group via the Pauli grading (the elements of SL(2,C) expressed by direct sum of unit matrix and generators of SU(2) group), we grade the SL(3,C) group with the generators of SU(3), i. e. the Gell-Mann matrices, then express the SU(3) group in terms of three SU(2) subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL(2,C). If the mapping from group SL(3,C) to the Lorentz group is constructed by choosing one SU(2) subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex γ_μ \vpartial^μ is extended to encompass γ₅γ_μ\vpartial^μ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.

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Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

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