Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions

TL;DR

This paper introduces a noncommutative extension of ideal fluid dynamics in 3+1 dimensions, revealing multi-parameter central extensions, vorticity generation, and non-isentropic behavior, challenging previous beliefs about Galilean symmetries.

Contribution

It presents the first noncommutative 3+1D fluid model with multi-parameter central extensions and explores its novel physical features.

Findings

Multi-parameter central extension in 3+1D Galilean algebra.

Noncommutativity induces vorticity in irrotational fluids.

The model exhibits non-barotropic, non-isentropic behavior.

Abstract

A noncommutative extension of an ideal (Hamiltonian) fluid model in $3+1$-dimensions is proposed. The model enjoys several interesting features: it allows a multi-parameter central extension in Galilean boost algebra (which is significant being contrary to existing belief that similar feature can appear only in $2+1$-dim.); noncommutativity generates vorticity in a canonically irrotational fluid; it induces a non-barotropic pressure leading to a non-isentropic system. (Barotropic fluids are entropy preserving as pressure depends only on matter density.) Our fluid model is termed "Exotic" since it has close resemblance with the extensively studied planar (2+1-dim.) Exotic models and Exotic (noncommutative) field theories.