Quantum dynamics of perfect fluids

TL;DR

This paper investigates the quantum field theory of perfect fluids, focusing on vortex modes and their contributions to stress tensor correlators, using semi-classical states to address infrared issues and enable perturbative calculations.

Contribution

It introduces a method to compute correlators in quantum perfect fluids using semi-classical states, overcoming challenges posed by vortex modes and their zero dispersion.

Findings

Vortex modes contribute non-trivially to stress tensor correlators.

Semi-classical states serve as an effective infrared regulator.

Perturbation theory can be applied to quantum fluids with vortex modes.

Abstract

We study the quantum field theory of zero temperature perfect fluids. Such systems are defined by quantizing a classical field theory of scalar fields $\phi^I$ that act as Lagrange coordinates on an internal spatial manifold of fluid configurations. Invariance under volume preserving diffeomorphisms acting on these scalars implies that the long-wavelength spectrum contains vortex (transverse modes) with an exact $\omega_T=0$ dispersion relation. As a consequence, physically interpreting the results obtained via perturbative quantization of this theory has proven to be challenging. In this paper, we show that correlators evaluated in a class of semi-classical (Gaussian) initial states prepared at $t=0$ are well-defined and accessible via perturbation theory. The width of the initial state effectively acts as an infrared regulator without explicitly breaking diffeomorphism invariance of the classical action. As an application, we compute the stress tensor two-point correlators and show that vortex modes give a non-trivial contribution to the response function, non-local in both space and time.