宏观离散量子宇宙学

摘要：

对于米尔恩的基于洛伦兹群的时空和这个群的盖尔芬德-奈马克酉表示，我们将一个由“宇宙学前子”--量子论宇宙成分--组成的福克空间联系起来。米尔恩的“宇宙学原理”依赖于“年龄”--全球时间--的洛伦兹不变性。我们把米尔恩的时空划分成年龄上固定宏观宽度的“切片”，而“宇宙射线”定义在（双曲）切片边界上--福克空间只与这些特殊的宇宙年龄有关。每个（固定年龄）前子位于一个6维流形内，其3个“额外”维度之一在狄拉克意义上与表示前子（连续）局部时间的自伴算子相关联，算子正则共轭表示前子（总）能量。在任何时空片边界上的自伴算符期望，在接下来的时空片中规定了一个无涨落的“世俗现实”--电磁势和引力势“拴在”局部守恒的电荷和能量动量的电流密度上。在一个切片的上边界处的射线是从下边界射线确定的分支切片遍历费曼路径进行（无发散）潜在的依赖作用。一个宏观稳定的正能量单前子波函数要么等同于标准模型基本粒子，要么等同于引力子。在中等密度的宇宙区域，如太阳系，重复测量是有意义的，狭义相对论-庞加莱不变性-是准确的时空尺度远低于哈勃和普朗克。

英文摘要：

To Milne's Lorentz-group-based spacetime and Gelfand-Naimark unitary representations of this group we associate a Fock space of 'cosmological preons'-quantum-theoretic universe constituents. Milne's 'cosmological principle' relies on Lorentz invariance of 'age'--global time. We divide Milne's spacetime into 'slices' of fixed macroscopic width in age, with 'cosmological rays' defined on (hyperbolic) slice boundaries-Fock space attaching only to these exceptional universe ages. Each (fixed-age) preon locates within a 6-dimensional manifold, one of whose 3 'extra' dimensions associates in Dirac sense to a self-adjoint operator that represents preon (continuous) local time, the operator canonically-conjugate thereto representing preon (total) energy. Self-adjoint-operator expectations at any spacetime-slice boundary prescribe throughout the following slice a non-fluctuating 'mundane reality'- electromagnetic and gravitational potentials 'tethered' to current densities of locally-conserved electric charge and energy-momentum. The ray at the upper boundary of a slice is determined from the lower-boundary ray by branched slice-traversing Feynman paths that carry (divergence-free) potential-depending action. A macroscopically-stable positive-energy single-preon wave function identifies either with a Standard-Model elementary particle or with a graviton. Within intermediate-density universe regions such as the solar system, where reproducible measurement is meaningful, special relativity--Poincaré invariance-is accurate for spacetime scales far below that of Hubble and far above that of Planck.

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