动态生成基本粒子质量的Dirac表示
Dirac Representation of Dynamically-Generated Elementary-Particle Mass
摘要：
特殊相对论动力学生成的基本粒子质量由作用在6维欧氏群流形上的函数的操纵希尔伯特空间（RHS）上的自伴能量算符表示。能量算符不是经典时间中无穷小波函数演化的生成元。光线演化是由带有作用的费曼路径产生的。扩展量子理论的形式主义，狄拉克发明和应用非相对论，酉庞加莱群表示提供了一个类空实体，我们称之为“前子”的波函数。虽然术语“前子可观测”是误导性的，但六个连续的费曼路径接触前子坐标指定了空间位置（3个坐标），类光速度方向（2个坐标）和横向偏振（1个坐标）。速度和空间位置结合起来定义一个前子的时间算子共轭的能量算子。在群流形上的RHS基函数中，波函数依赖于一个前子“速度-螺旋度”整数或半奇数）和一个类光速度4-向量，该速度4-向量与一对正则共轭的类空4-向量洛伦兹正交。一个4-矢量规定了前子在时空中的位置，而它的共轭规定了前子的能量-动量。任何自旋（正类时）基本粒子的质量都伴随着前子类光速度和速度螺旋度的反射对称波动，这与狄拉克的“相对论”电子的薛定谔称之为“zitterbewegung”相似。但是（与狄拉克不同），一个微小的基本粒子“纵向”空间延伸伴随着前子纵向动量的巨大波动，这是由关于垂直于自旋方向的平面的不动粒子反射对称性决定的。
英文摘要：
Special-relativistic dynamically-generated elementary-particle mass is represented by a self-adjoint energy operator acting on a rigged Hilbert space (RHS) of functions over the 6-dimensional Euclidean-group manifold. The energy operator is not the generator of infinitesimal wave-function evolution in classical time. Ray evolution is generated by action-carrying Feynman paths. Extending quantum-theoretic formalism which Dirac invented and applied non-relativistically, unitary Poincaré -group representation is provided by the wave functions of a spacelike entity that we call 'preon'. Although the term 'preon observable' is misleading, six continuous Feynman-path-contacting preon coordinates specify spatial location (3 coordinates), lightlike-velocity-direction (2 coordinates) and transverse polarization (1 coordinate). Velocity and spatial location combine to define a preon time operator conjugate to the energy operator. In RHS bases alternative to functions over the group manifold, the wave function depends on a preon 'velocity-helicity' integer or half-odd integer) and a positive-lightlike velocity 4-vector that is Lorentz-orthogonal to a canonically-conjugate pair of spacelike 4-vectors. One 4-vector prescribes location in preon spacetime while its conjugate prescribes preon energy-momentum. Emulating the Schrödinger-dubbed 'zitterbewegung' of Dirac's 'relativistic' electron, mass for any spinning (positive-timelike) elementary particle accompanies a reflection-symmetric fluctuation of preon lightlike velocity and velocity-helicity. But (departing from Dirac), a tiny elementary-particle 'longitudinal' spatial extension accompanies a huge fluctuation of preon longitudinal momentum dictated by motionless-particle reflection symmetry about the plane perpendicular to spin direction.
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