General coordinate invariance in quantum many-body systems

Abstract

We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the background metric and gauge fields, first introduced by Son and Wingate in 2005 and refined in subsequent works, follow naturally from our framework. Our approach makes it clear that Galilei or Poincare symmetry is by no means a necessary prerequisite for making the theory invariant under coordinate diffeomorphisms. General covariance merely expresses the freedom to choose spacetime coordinates at will, whereas the true, physical symmetries of the system can be separately implemented as "internal" symmetries within the vielbein formalism. A systematic way to implement such symmetries is provided by the coset construction. We illustrate this point by applying our formalism to nonrelativistic s-wave superfluids.

14 pages; v2: minor update with additional references and acknowledgments, version to appear in Phys. Rev. D

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Cited by in corpus (33)

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• Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
• Lifshitz Space-Times for Schroedinger Holography
• Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
• On the coupling of Galilean-invariant field theories to curved spacetime
• Revisiting non-relativistic limits
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• Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
• Spatially isotropic homogeneous spacetimes
• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Mutual Interactions of Phonons, Rotons, and Gravity
• Torsional Newton-Cartan Geometry from the Noether Procedure
• Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation
• Torsional Newton-Cartan geometry from Galilean gauge theory
• Effective field theory for spacetime symmetry breaking
• Anomalies for Galilean fields
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Galilean Anomalies and Their Effect on Hydrodynamics
• Galilean invariance at quantum Hall edge
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• More On Nonrelativistic Diffeomorphism Invariance
• Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
• Hydrodynamic effective field theories with discrete rotational symmetry
• Hall viscosity, spin density, and torsion
• Gravitational anomalies on the Newton-Cartan background
• Nonrelativistic hydrodynamics from quantum field theory: (I) Normal fluid composed of spinless Schrödinger fields
• Gauging nonrelativistic field theories using the coset construction
• More on the operator-state map in non-relativistic CFTs
• Exceptional nonrelativistic effective field theories with enhanced symmetries
• Non-relativistic fluids on scale covariant Newton-Cartan backgrounds
• Galilean Geometry in Condensed Matter Systems
• Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories
• On Twisted Spacetimes: a new class of Galilean cosmological models