Spinors in non-relativistic Chern-Simons electrodynamics

Abstract

It is shown that the non-relativistic `Dirac' equation of Lévy-Leblond, we used recently to describe a spin $1/2$ field interacting non-relativistically with a Chern-Simons gauge field, can be obtained by lightlike reduction from $3+1$ dimensions. This allows us to prove that the system is Schrödinger symmetric. A spinor representation of the Schrödinger group is presented. Static, self-dual solutions, describing spinor vortices are given and shown to be the non-relativistic limits of the fermionic vortices found by Cho et al. The construction is extended to external harmonic and uniform magnetic fields.

Plain TEX, 43 pages

Cited by in corpus (40)

• Non-relativistic conformal symmetries and Newton-Cartan structures
• The geometry of Schrödinger symmetry in non-relativistic CFT
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Vortices in (abelian) Chern-Simons gauge theory
• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie Symmetries of the Lévy-Leblond Equations
• Bosons, fermions and anyons in the plane, and supersymmetry
• Planar Carrollean dynamics, and the Carroll quantum equation
• Affine Extension of Galilean Conformal Algebra in 2+1 Dimensions
• Embedding nonrelativistic physics inside a gravitational wave
• Aspects of Non-Relativistic Quantum Field Theories
• Curvatronics with bilayer graphene in an effective $4D$ spacetime
• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
• Fermions in non-relativistic AdS/CFT correspondence
• Conformal Killing Tensors and covariant Hamiltonian Dynamics
• Galilean noncommutative gauge theory: symmetries & vortices
• Schrödinger symmetry: a historical review
• A family of super Schrodinger invariant Chern-Simons matter systems
• Galilean Field Theories and Conformal Structure
• Fermions and the Sch/nrCFT Correspondence
• Supersymmetry of the planar Dirac - Deser-Jackiw-Templeton system, and of its non-relativistic limit
• On the Schr{ö}dinger-Newton equation and its symmetries: a geometric view
• Quantization of Interacting Galilean Field theories
• Trace anomaly for non-relativistic fermions
• Electronic properties of curved few-layers graphene: a geometrical approach
• Path-integral quantization of Galilean Fermi fields
• Non-relativistic Reduction of Spinors, New Currents and their Algebra
• Vortices in Maxwell-Chern-Simons-Higgs models with nonminimal coupling
• Galilean fermions: Classical and quantum aspects
• Vortex Solutions of Nonrelativistic Fermion and Scalar Field Theories Coupled to Maxwell-Chern-Simons theories
• Remarks on the solutions of the Maxwell- Chern-Simons theories
• On the Lévy-Leblond-Newton equation and its symmetries: a geometric view
• Vortex in Maxwell-Chern-Simons models coupled to external backgrounds
• Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
• Spin operator and spin states in Galilean covariant Fermi field theories
• Solutions for the Lévy-Leblond or parabolic Dirac equation and its generalizations
• Vortex Solutions of Four-fermion Theory coupled to a Yang-Mills-Chern-Simons Gauge Field
• Analytic solution for Gauged Dirac-Weyl equation in $(2+1)$-dimensions
• Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets
• Lévy-Leblond Equation and Eisenhart-Duval lift in Koopman-von Neumann Mechanics