The quantum mechanics of perfect fluids

TL;DR

This paper explores the quantum properties of perfect fluids, revealing peculiar vortex behaviors, a vanishing strong-coupling scale, and implications for the theory's validity and unitarity.

Contribution

It introduces a quantum field theory framework for fluids, highlighting vortex effects and their impact on the theory's strong-coupling and ground state structure.

Findings

Vortices have a vanishing strong-coupling energy scale.

An analog of Coleman's theorem shows no quantum vacuum counterpart.

Vortices disrupt the link between short distances and high energies.

Abstract

We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vortex degrees of freedom. On the one hand, these have formally a vanishing strong-coupling energy scale, thus suggesting that the effective theory's regime of validity is vanishingly narrow. On the other hand, we prove an analog of Coleman's theorem, whereby the semiclassical vacuum has no quantum counterpart, thus suggesting that the vortex premature strong-coupling phenomenon stems from a bad identification of the ground state and of the perturbative degrees of freedom. Finally, vortices break the usual connection between short distances and high energies, thus potentially impairing the unitarity of the effective theory.