Acoustic versus electromagnetic field theory: scalar, vector, spinor representations and the emergence of acoustic spin

TL;DR

This paper introduces a new Lagrangian framework for acoustic fields that captures vector properties and spin, drawing analogies with electromagnetic theory, and proposes a spinor representation that unifies scalar and vector descriptions.

Contribution

It develops a novel Lagrangian formulation for acoustic fields incorporating vector potentials and spin, and introduces a spinor representation inspired by electromagnetic duality.

Findings

Derived canonical momentum and spin densities as conserved currents.

Demonstrated the ability to describe nonzero acoustic spin angular momentum.

Established analogies between acoustic and electromagnetic field theories.

Abstract

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a ${\it scalar}$ potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement ${\it vector}$ potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential representations, we put forward an acoustic ${\it spinor}$ representation combining the scalar and vector representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.