Polar Duality Between Pairs of Transverse Lagrangian Planes. Applications to Uncertainty Principles

TL;DR

This paper extends polar duality to pairs of transverse Lagrangian planes in symplectic space, providing a geometric interpretation and applying it to quantum uncertainty principles.

Contribution

It introduces a novel extension of polar duality to transverse Lagrangian planes and links it to symplectic geometry and quantum indeterminacy.

Findings

Polar duality can be interpreted within symplectic geometry.

The extension offers new insights into quantum uncertainty principles.

Provides a geometric framework connecting duality and quantum mechanics.

Abstract

We extend the notion of polar duality to pairs of transverse Lagrangian planes in the standard symplectic space. This allows us to show that polar duality has a natural interpretation in terms of symplectic geometry. We apply our results to the quantum principle of indeterminacy.