Supersymmetric Fluid Mechanics

TL;DR

This paper introduces a supersymmetric extension of fluid mechanics by incorporating Grassmann variables, leading to a model where vorticity arises naturally and supersymmetry is achieved through specific interactions.

Contribution

It develops a novel supersymmetric fluid model by integrating Grassmann variables, revealing new mechanisms for vorticity and symmetry in fluid dynamics.

Findings

Grassmann variables induce non-zero vorticity in irrotational flows.

Supersymmetry is realized through specific Grassmann interactions.

The model provides a new framework linking fluid mechanics and supersymmetry.

Abstract

When anticommuting Grassmann variables are introduced into a fluid dynamical model with irrotational velocity and no vorticity, the velocity acquires a nonvanishing curl and the resultant vorticity is described by Gaussian potentials formed from the Grassmann variables. Upon adding a further specific interaction with the Grassmann degrees of freedom, the model becomes supersymmetric.