Geodesic
Discrete transformations in a~six-dimensional model of Minkowski space
Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 3, pp. 366-371

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An analysis of the invariance properties of the equation for a massless particle in the sixdimensional Dirac model reveals the existence of two types of neutrino; these may be called conventionally the plus and minus neutrino. Reflections in the six-dimensional space are intimately connected with the operation $R$: $$ Rx^{\mu}=\frac{x^{\mu}}{(x,x)} $$ of inversion in the unit hypersphere in the Minkowski space. An operation $K$ which transforms a plus neutrino into a minus neutrino and vice versa is introduced. It may be conjectured that the existence of the plus and minus neutrino reflects the existence in nature of the electron and the muon neutrino. 
@article{TMF_1970_5_3_a4,
     author = {B. G. Konopelchenko},
     title = {Discrete transformations in a~six-dimensional model of {Minkowski} space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {366--371},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_5_3_a4/}
}
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B. G. Konopelchenko. Discrete transformations in a~six-dimensional model of Minkowski space. Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 3, pp. 366-371. http://geodesic.mathdoc.fr/item/TMF_1970_5_3_a4/