论文标题
我们可以从Klein-Gordon方程的共形非传染性中学到什么？
What can we learn from the conformal noninvariance of the Klein-Gordon equation?
论文作者
论文摘要
众所周知，弯曲时空中的klein-gordon方程在有或没有质量项的情况下都是共形的无变化的。我们表明，这种非传染性提供了不同级别的非平凡的物理见解，首先是在完全相对论的制度内，然后在非宗派主义方程式中，然后在schrödinger方程式中，然后在de broglie-bohm的量子力学解释中。在存在带电电流的情况下，麦克斯韦方程的共形不变性面临着klein-gordon方程与矢量电势的共形非传染性。然后根据Maxwell方程的共形不变性检查了非最小耦合的klein-gordon方程与重力的保形不变性。最后，讨论了方程式在弯曲时空中aharonov-bohm效应的不变性的结果。
It is well known that the Klein-Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels, first within the fully relativistic regime, then in the nonrelativistic regime leading to the Schrödinger equation, and then within the de Broglie-Bohm causal interpretation of quantum mechanics. The conformal noninvariance of the Klein-Gordon equation coupled to a vector potential is confronted with the conformal invariance of Maxwell's equations in the presence of a charged current. The conformal invariance of the non-minimally coupled Klein-Gordon equation to gravity is then examined in light of the conformal invariance of Maxwell's equations. Finally, the consequence of the noninvariance of the equation on the Aharonov-Bohm effect in curved spacetime is discussed.
