Symmetries and Couplings of Non-Relativistic Electrodynamics
arXiv:1607.01753
Abstract
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galilei algebra plus two dilatations remain. Hence one can scale time and space independently, allowing Lifshitz scale symmetries for any value of the critical exponent .
arXiv comment26 pages; v2 references added
References in corpus (28)
- Celestial Mechanics, Conformal Structures, and Gravitational Waves
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- Torsional Newton-Cartan Geometry and Lifshitz Holography
- Gauging the Carroll Algebra and Ultra-Relativistic Gravity
- Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
- Warped Conformal Field Theory
- Spacetime Symmetries of the Quantum Hall Effect
- Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
- Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics
- Lifshitz Gravity for Lifshitz Holography
- Lifshitz Space-Times for Schroedinger Holography
- Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
- Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
- Newton-Cartan Geometry and the Quantum Hall Effect
- Three-Dimensional Extended Bargmann Supergravity
- Newton-Cartan Supergravity
- Revisiting non-relativistic limits
- Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
- On the electrodynamics of moving bodies at low velocities
- String theory embeddings of non-relativistic field theories and their holographic Horava gravity duals
- Torsional Newton-Cartan Geometry from the Noether Procedure
- Torsional Newton-Cartan Geometry and the Schrödinger Algebra
- On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics
- Galilean Yang-Mills Theory
- The Non-Relativistic Superparticle in a Curved Background
- Newton-Cartan supergravity with torsion and Schrödinger supergravity
- Spinor fields in general Newton-Cartan backgrounds
- Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity