Torsion, magnetic monopoles and Faraday's law via a variational principle

9th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Mannheim, Philip D.^1

Department of Physics, University of Connecticut, Storrs

CT

06269, United States^1

关键词: Axial vector;    Faraday's laws;    Magnetic monopoles;    Path integral;    Riemannian geometry;    Stationarity;    Variational principles;    Vector potential;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/615/1/012004/pdf
DOI  :  10.1088/1742-6596/615/1/012004

来源: IOP

【 摘 要 】

Even though Faraday's Law is a dynamical law that describes how changing E and B fields influence each other, by introducing a vector potential Aμaccording to Fμν= ∂νAν- ∂νAμFaraday's Law is satisfied kinematically, with the relation (-g)-1/2μνστ∇νFστ= 0 holding on every path in a variational procedure or path integral. In a space with torsion Qαβγthe axial vector Sμ= (-g)1/2μαβγQαβγserves as a chiral analog of Aμ, and via variation with respect to Sμone can derive Faraday's Law dynamically as a stationarity condition. With Sμserving as an axial potential one is able to introduce magnetic monopoles without Sμneeding to be singular or have a non-trivial topology. Our analysis permits torsion and magnetic monopoles to be intrinsically Grassmann, which could explain why they have never been detected. Our procedure permits us to both construct a Weyl geometry in which Aμis metricated and then convert it into a standard Riemannian geometry.