General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

Details General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

2005-09-29

arxiv.org/abs/cond-mat/0509786v2

Annals Phys. 321 (2006) 197-224

Physics

Condensed Matter

Other Condensed Matter

33 pages, 2 figures; v2: small typos fixed, references added

Scientific paper

10.1016/j.aop.2005.11.001

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.

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