Aspects of Non-Relativistic Quantum Field Theories

Abstract

Non-relativistic quantum field theory is a framework that describes systems where the velocities are much smaller than the speed of light. A large class of those obey Schrödinger invariance, which is the equivalent of the conformal symmetry in the relativistic world. In this review, we pedagogically introduce the main theoretical tools used to study non-relativistic physics: null reduction and $c\to \infty$ limits, where $c$ is the speed of light. We present a historical overview of non-relativistic wave equations, Jackiw-Pi vortices, the Aharonov-Bohm scattering, and the trace anomaly for a Schrödinger scalar. We then review modern developments, including fermions at unitarity, the quantum Hall effect, off-shell actions, and a systematic classification of the trace anomaly. The last part of this review is dedicated to current research topics. We define non-relativistic supersymmetry and a corresponding superspace to covariantly deal with quantum corrections. Finally, we define the Spin Matrix Theory limit of the AdS/CFT correspondence, which is a non-relativistic sector of the duality obtained via a decoupling limit, where a precise matching of the two sides can be achieved.

96 pages, 4 figures, review article; v2: matching the journal version with small improvements and added citations

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Cited by in corpus (13)

• Worldsheet Formalism for Decoupling Limits in String Theory
• Schrödinger symmetry: a historical review
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Non-Relativistic Holography from AdS${}_5$/CFT${}_4$
• Non-relativistic trace anomaly and equation of state in dense fermionic matter
• Setting the connection free in the Galilei and Carroll expansions of gravity
• Quantum Field Theory of Electrons and Nuclei
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Precise correspondence between the p-wave chiral superfluid and the spinless bosonic superfluid in the lowest Landau level
• Beyond Born-Oppenheimer Green's function theories: absolute and relational
• Fast-forward scaling theory for quantum dynamics on curved space-time
• Gauge interactions and the Galilean limit