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arXiv 0901.2896hep-th
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非相对论相空间的对称性与夸克-轻子产生的结构

Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation

Piotr Zenczykowski

备注：
Proceedings of DICE2008, Castiglioncello, Italy, 22nd-26th September 2008
发表信息：
J.Phys.Conf.Ser.174:012032,2009
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摘要：

根据哈密顿形式主义，非相对论性相空间可以被视为物理学的舞台，动量和位置被视为独立变量。于是，x^2+p^2的不变性构成了普通旋转不变性的自然推广。我们考虑这种形式的狄拉克线性化，位置和动量满足标准的对易关系。这导致了一个量子级结构的识别，从一些相空间属性可能会出现。相空间中真正的旋转和反射与新的量子数的存在有关，与普通的3D空间无关。它们的性质使它们与表征标准模型中单个夸克-轻子生成结构的内部量子数一致。特别是，基本粒子的Harari-Shirtson前子模型的代数结构被精确地再现，并且没有调用任何子。对非相对论性相空间的克利福德代数的分析挑出了一个可能与轻子质量概念有关的元素。这个元素被转化为对应于单色夸克的元素，导致了质量概念的推广和夸克不可观测性讨论的不同出发点。

英文摘要：

According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.

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