Symmetries and currents of the ideal and unitary Fermi gases
arXiv:1111.3656 · doi:10.1007/JHEP02(2012)113
Abstract
The maximal algebra of symmetries of the free single-particle Schroedinger equation is determined and its relevance for the holographic duality in non-relativistic Fermi systems is investigated. This algebra of symmetries is an infinite dimensional extension of the Schroedinger algebra, it is isomorphic to the Weyl algebra of quantum observables, and it may be interpreted as a non-relativistic higher-spin algebra. The associated infinite collection of Noether currents bilinear in the fermions are derived from their relativistic counterparts via a light-like dimensional reduction. The minimal coupling of these currents to background sources is rewritten in a compact way by making use of Weyl quantisation. Pushing forward the similarities with the holographic correspondence between the minimal higher-spin gravity and the critical O(N) model, a putative bulk dual of the unitary and the ideal Fermi gases is discussed.
67 pages, 2 figures; references added, minor improvements in the presentation, version accepted for publication in JHEP
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- The Non-Relativistic Geometric Trinity of Gravity
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- Underdetermination in Classic and Modern Tests of General Relativity
- Constrained Hamiltonian analysis of a non relativistic Schrodinger field coupled with C-S gravity
- Higher spin holography with Galilean symmetry in general dimensions
- Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory