Quantum Field Theory of Fluids

The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is “freer”, in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.

Figure 1

The $O(w_0^{-2})$ diagrams for the correlator $⟨(\sqrt{B}{u}^0-1)(\sqrt{B}{u}^0-1)⟩$.

Figure 2

Contours of equal one-loop and tree-level absolute contributions to the momentum-space two-point correlator $⟨(\sqrt{B}{u}^0-1)(\sqrt{B}{u}^0-1)⟩$, for various $O(1)$ values of $c$ and $f_3$.