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arXiv 1609.07095hep-phhep-thmath-phmath.MP
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有质量和无质量中微子的对称性

Symmetries of Massive and Massless Neutrinos

Y. S. Kim

摘要:

维格纳的小群是洛伦兹群的子群,洛伦兹群规定了有质量和无质量粒子的内部时空对称性。对于有质量和无质量的粒子,这些小群分别类似于O(3)和E(2)。虽然O(3)对称的几何是我们所熟悉的,但平面几何不能解释无质量粒子的类E(2)对称。然而,圆柱的几何形状可以用螺旋度和规范自由度来解释对称性。进一步证明了无质量粒子的对称性可以作为有质量粒子类O(3)对称性的零质量极限来得到。进一步表明,无质量中微子的极化是规范不变性的结果,而有质量中微子的对称性仍类似于O(3)。

英文摘要:

Wigner's little groups are subgroups of the Lorentz group dictating the internal space-time symmetries of massive and massless particles. These little groups are like O(3) and E(2) for massive and massless particles respectively. While the geometry of the O(3) symmetry is familiar to us, the geometry of the flat plane cannot explain the E(2)-like symmetry for massless particles. However, the geometry of a circular cylinder can explain the symmetry with the helicity and gauge degrees of freedom. It is shown further that the symmetry of the massless particle can be obtained as a zero-mass limit of O(3)-like symmetry for massive particles. It is shown further that the polarization of massless neutrinos is a consequence of gauge invariance, while the symmetry of massive neutrinos is still like O(3).

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