Spin Angular Momentum in Acoustic Field Theory

We construct a Lagrangian representation of acoustic field theory that accounts for the local radiation forces and torques experienced by subwavelength probe particles, analogous to those experienced by Rayleigh particles in optical fields. The traditional acoustic Lagrangian representation with a scalar potential is unable to reproduce these measured effects. By introducing a displacement vector potential, analogous to the electromagnetic vector potential, we derive the appropriate local momentum and spin densities directly as conserved Noether currents. The results agree with those proposed in recent analyses of intrinsic acoustic spin and are consistent with recent experiments.