Conformal Fluid Dynamics

TL;DR

This paper develops a conformal, dissipationless relativistic fluid theory in 2D, exploring its algebraic structure, canonical formulation, and quantum challenges, contributing to the understanding of 2D conformal fluid dynamics.

Contribution

It introduces a conformal 2D fluid model with a novel algebraic structure and provides a canonical framework, addressing quantum quantization issues.

Findings

Representation of 2D area-preserving diffeomorphisms in the fluid

Calculation of the current algebra's central charge

Discussion of quantum operator ordering problems

Abstract

We present a conformal theory of a dissipationless relativistic fluid in 2 space-time dimensions. The theory carries with it a representation of the algebra of 2-$D$ area-preserving diffeomorphisms in the target space of the complex scalar potentials. A complete canonical description is given, and the central charge of the current algebra is calculated. The passage to the quantum theory is discussed in some detail; as a result of operator ordering problems, full quantization at the level of the fields is as yet an open problem.