Alternative Expression for the Electromagnetic Lagrangian

作者：Saldanha Pablo L^*

来源：Brazilian Journal of Physics, 2016, 46(3): 316-320.

DOI：10.1007/s13538-016-0417-4

• Aharonov-Bohm effect
• Lagrangian dynamics
• Foundations of electromagnetism
• Foundations of quantum mechanics

We reintroduce an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields, proposed by Livens about one century ago. This Lagrangian is written in terms of the local superposition of the particle fields with the applied electromagnetic fields, not in terms of the particle charge and of the electromagnetic potentials as is usual. Here, we show that the total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. We also show that the alternative Lagrangian is equivalent to the traditional one in their domain of validity and that it provides an interesting description of the Aharonov-Bohm effect.

• 出版日期2016-6