有质量带电自旋粒子的相对论Hamilton-Jacobi方程及其等价Dirac方程和de Broglie-Bohm理论
The Relativistic Hamilton-Jacobi Equation for a Massive, Charged and Spinning Particle, its Equivalent Dirac Equation and the de Broglie-Bohm Theory
摘要：
利用Clifford和Spin-Clifford形式主义，我们证明了一个带电的大质量（和自旋）粒子与外部电磁场相互作用的经典相对论性Hamilton Jacobi方程等价于一类旋量场所满足的Dirac-Hestenes方程，我们称之为经典旋量场，其特征在于具有Takabayashi角函数常数（等于0或π）.我们还研究了一类来自于广义经典旋量场的非线性Dirac-Hestenes类方程。最后我们证明了一般的Dirac-Hestenes方程（它是通常Dirac方程的Clifford丛的代表）给出了一个广义的Hamilton-Jacobi方程，其中量子势满足严格的约束，“粒子的质量”成为一个变量。我们的结果可以解释德布罗意-玻姆理论的预测和最近的实验之间的实验差异。我们还简要讨论了德布罗意的双重解决方案的理论，鉴于我们的结果表明，它可以实现，至少在自旋自由粒子的情况下。本文包含几个附录中的符号和证明的一些结果的文本。
英文摘要：
Using the Clifford and the Spin-Clifford formalisms we prove that the classical relativistic Hamilton Jacobi equation for a charged massive (and spinning) particle interacting with an external electromagnetic field is equivalent to a Dirac-Hestenes equation satisfied by a class of spinor fields that we call classical spinor fields, characterized for having the Takabayashi angle function constant (equal to 0 or π). We also investigate a nonlinear Dirac-Hestenes like equation that comes from some class of generalized classical spinor fields. Finally we show that the general Dirac-Hestenes equation (which is a representative in the Clifford bundle of the usual Dirac equation) gives a generalized Hamilton-Jacobi equation where the quantum potential satisfy a severe constraint and the "mass of the particle" becomes a variable. Our results can then explain the experimental discrepancies found between prediction of the de Broglie-Bohm theory and recent experiments. We briefly discuss also the de Broglie's double solution theory in view of our results showing that it can be realized, at least in the case of spinning free particles..The paper contains several Appendices where notation and proofs of some results of the text are presented.
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