量子场的几何表述
Geometrical formulation of quantum fields
摘要：
量子力学的路径积分公式将与粒子相关联的波函数定义为相因子之和，相因子是经典作用量的周期函数。在本文章中，这种周期性示出赋予相应的周期性的弧长用于parameterized轨迹的平移所产生的波函数的一个参数的家庭。将平移参数附加到基上，得到一个扩张流形。利用波函数族相对于平移参数的周期性以及由路径积分公式推导出的广义Klein-Gordon方程的解，定义了一个以粒子为量子的扩展流形中真空能量为零的量子化场.在扩展的高维空间中，利用粒子的性质，得到了本质上相同粒子的经典描述。该流形可以在该处理中取代基底，以继续该过程中生成的高维流形的程序。以三维欧氏空间为基，给出了光子在基空间中的经典和量子粒子描述，以及与闵可夫斯基时空一致的扩展流形中的场描述.场公式产生量子化的麦克斯韦方程组。一个新的解释时间作为相应的翻译参数的结果在这个过程中。扩展流形中的经典描述，即，闵可夫斯基时空，导致相对论描述的一个大质量粒子有关的光子。结果进一步说明了这种大质量粒子在闵可夫斯基时空中获得平行的结果。
英文摘要：
Path integral formulation of quantum mechanics defines the wavefunction associated with a particle as a sum of phase-factors, which are periodic functions of classical action. In the present article, this periodicity is shown to impart the corresponding periodicity to a one parameter family of wavefunctions generated by the translations of arclength used to parameterize the trajectories. Translation parameter is adjoined to the base to obtain an extended manifold. Periodicity of the family of wavefunctions with respect to the translation parameter together with solutions of the generalized Klein-Gordon equation, which is deducible from the path integral formulation, is used to define a quantized field with zero vacuum energy in the extended manifold with the particle being its quantum. Classical description of essentially the same particle is obtained in the extended higher dimensional space using its properties. This manifold can replace the base in this treatment to continue the program for higher dimensional manifolds generated in the process. Results are illustrated by taking the three-dimensional Euclidean space the base, which yields the classical and quantum particle descriptions of photon in the base and the field description in the resulting extended manifold, which is identified with the Minkowski spacetime. The field formulation yields the quantized Maxwell's equations. A novel interpretation of time as the corresponding translation parameter results in the process. Classical description in the extended manifold, i.e., the Minkowski spacetime, results in the relativistic description of a massive particle related to the photon. The results are further illustrated for this massive particle in the Minkowski spacetime obtaining parallel results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
