Energy-momentum conservation and Lipkin's zilch

TL;DR

This paper develops a method to identify symmetries associated with Lipkin's zilch and energy-momentum conservation laws in n-dimensional Minkowski space-time, linking them to physical quantities like optical chirality.

Contribution

It introduces a new approach to determine symmetries of zilch and energy-momentum conservation laws, extending the understanding of these symmetries in higher-dimensional space-times.

Findings

Derived relations between zilch tensor and current-density in n-dimensional space

Extended symmetry calculation method to energy-momentum conservation

Reduced optical chirality equations to known continuity equations in 4D

Abstract

As Noether's theorem states any differentiable symmetry of the action of a physical system has a corresponding conservation law. Lipkin introduced the conservation laws of zilches. But the corresponding symmetries are yet to be determined. Here we find a method to determine those symmetries and by direct calculations express the zilch tensor's relation to current-density for $n$-dimensional Minkowski space-time. Also, we extend this method to calculate symmetries of conservation of energy-momentum. Finally we show that in the special case of n=4, our general equation governing optical chirality reduces to the continuity equation of optical chirality density and optical chirality flow.