Quantum dynamics of perfect fluids

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 $ϕ^I$ 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 $ω_T=0$ 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.