标题： 从光子到麦克斯韦方程。 关于量子力学中光子局域性和光子轨迹的思考——在德布罗意-玻姆诠释中的探讨 显示英文标题

标题： From the Photon to Maxwell Equation. Ponderations on the Concept of Photon Localizability and Photon Trajectory in a de Broglie-Bohm Interpretation of Quantum Mechanics

摘要： In this paper using the Clifford bundle formalism we show how starting from the photon concept and its relativistic Hamilton-Jacobi equation (HJE) we immediately get (with a simple hypothesis concerning the form of the photon canonical momentum) Maxwell equation (ME) satisfied by a null $2$-form field $\boldsymbol{F}$ which is a plane wave solution (PWS) of ME. Moreover, we show how introducing a potential $1$-form $\boldsymbol{A}$ such that $\boldsymbol{F}=d\boldsymbol{A}$ we can see how a duality rotation changed in a spatial rotation transformation besides showing how $\mathrm{i}=\sqrt{-1}$ enters Maxwell theory thus permitting the writing of a representative of ME as Schrödinger like equation which plays a key role in answering one of the main questions addressed in this paper, namely: is there any sense in talking about photon trajectories in de Broglie-Bohm like theories? 为此，我们首先研究了麦克斯韦场$\mathbf{T}(n)$的能量动量\emph{扩展器}场在一些特殊情况下的性质，表明对于其中的一些情况，$\mathbf{T}_{0}=\mathbf{T}(\boldsymbol{\gamma}_{0})$甚至无法描述能量的流动。 提出了一种解决方案。 我们还证明，即使在真空中也存在脉冲重塑现象。 最后我们讨论了从量子场论得出的光子的薛定谔方程，并研究了一些作者认为暗示光子局域化的解。 我们讨论了这种想法是否有意义。 此外，我们表明，对于这些解，一旦接受光子波函数在空间和时间域都是扩展的，就可以推导出包含量子势的广义HJE，并且这可能导致自由空间中的非类光子轨迹。 我们简要讨论了我们的发现与最近实验的关系。 显示英文摘要

摘要： In this paper using the Clifford bundle formalism we show how starting from the photon concept and its relativistic Hamilton-Jacobi equation (HJE) we immediately get (with a simple hypothesis concerning the form of the photon canonical momentum) Maxwell equation (ME) satisfied by a null $2$-form field $\boldsymbol{F}$ which is a plane wave solution (PWS) of ME. Moreover, we show how introducing a potential $1$-form $\boldsymbol{A}$ such that $\boldsymbol{F}=d\boldsymbol{A}$ we can see how a duality rotation changed in a \ spatial rotation transformation besides showing how $\mathrm{i}=\sqrt{-1}$ enters Maxwell theory thus permitting the writing of a representative of ME as Schr\"{o}dinger like equation which plays a key role in answering one of the main questions addressed in this paper, namely: is there any sense in talking about photon trajectories in de Broglie-Bohm like theories? To this end we investigate first the nature of the energy-momentum \emph{extensor} field of the Maxwell field $\mathbf{T}(n)$ in some special situations showing that for some of those cases $\mathbf{T}_{0}=\mathbf{T}(\boldsymbol{\gamma}_{0})$ even cannot describe the flow of energy. A proposed solution is offered. We also prove that there exists a pulse reshaping phenomenon even in vacuum. Finally we discuss the Schr\"{o}dinger equation for a photon that follows from quantum field theory and investigate solutions that some authors think imply in photon localization. We discuss if such an idea is meaningful. Moreover, we show that for such solutions it is possible (once we accept that photon wave functions are extended in the space and also in the time domains) to derive a generalized HJE containing a quantum potential and which may lead to non lightlike photon trajectories in free space. We briefly discuss our findings in relation to a recent experiment.