CP破坏、大质量中微子及其手征凝聚：Snyder非对易几何的新结果
CP violation, massive neutrinos, and its chiral condensate: new results from Snyder noncommutative geometry
摘要：
非对易几何的Snyder模型由于最小尺度$\ell$（例如普朗克尺度或康普顿尺度）而产生爱因斯坦哈密顿约束内的$\ell^2$ -位移和自由狄拉克方程中的$γ^5$ -项，这明显违反CP对称性。本文重新考虑了Dirac方程。事实上，动量空间的闵可夫斯基双曲几何没有任何合理的修改理由。这是一致性-在物理学中，相空间，时空（坐标）和动量空间（动力学）是独立的数学结构。结果表明，修正的Dirac方程给出了左右手Weyl手征场的动力学质量产生机制，实现了中微子因CP破坏而获得质量的设想.结果表明，该模型等价于由两个2味质量场组成的规范场理论。整体手征对称性自发破缺为同位旋群导致了大量中微子的手征凝聚。这个结果超出了标准模型，但一般可以包含在基本粒子和基本相互作用的理论中。
英文摘要：
The Snyder model of a noncommutative geometry due to a minimal scale $\ell$, e.g. the Planck or the Compton scale, yields $\ell^2$-shift within the Einstein Hamiltonian constraint, and $γ^5$-term in the free Dirac equation violating CP symmetry manifestly. In this paper the Dirac equation is reconsidered. In fact, there is no any reasonable cause for modification of the Minkowski hyperbolic geometry of a momentum space. It is the consistency -- in physics phase space, spacetime (coordinates), and momentum space (dynamics) are independent mathematical structures. It is shown that the modified Dirac equation yields the kinetic mass generation mechanism for the left- and right-handed Weyl chiral fields, and realizes the idea of neutrinos receiving mass due to CP violation. It is shown that the model is equivalent to the gauge field theory of composed two 2-flavor massive fields. The global chiral symmetry spontaneously broken into the isospin group leads to the chiral condensate of massive neutrinos. This result is beyond the Standard Model, but in general can be included into the theory of elementary particles and fundamental interactions.
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