Compactified Reduction from Five to Four Space-Time Dimensions of the Antisymmetric Tensor Field

TL;DR

This paper applies Kaluza-Klein reduction to an antisymmetric tensor field in five dimensions, deriving a four-dimensional theory with coupled antisymmetric and vector fields, revealing new gauge invariances and charge interactions.

Contribution

It introduces a novel reduction method that couples four-dimensional antisymmetric and vector fields, uncovering modified Maxwell equations and gauge invariance in the reduced theory.

Findings

Electric charge current is conserved.

Source current of the antisymmetric field is generally not conserved.

Modified Maxwell equations include magnetic charge density and induced emf.

Abstract

We employ a Kaluza-Klein dimensional reduction process on the action of the antisymmetric tensor field in five-dimensional space-time. The result is a joint field theory of four-dimensional antisymmetric and vector fields. We write the inhomogeneous Euler-Lagrange equations and homogeneous Bianchi identity equations for the four dimensional field strengths. In these equations the terms that couple the field strengths depend on their variation with the compactified fifth variable. We find that the electric charge current is conserved, but in general the source current of the antisymmetric field is not. The action also displays joint gauge invariance. Observing the fields in a particular Lorentz frame leads to modified Maxwell and antisymmetric field equations. For the Maxwell field the antisymmetric field strengths lead to coupling terms that represent both magnetic charge density and additional induced emf.