A non-lorentzian primer

Abstract

We review both the kinematics and dynamics of non-lorentzian theories and their associated geometries. First, we introduce non-lorentzian kinematical spacetimes and their symmetry algebras. Next, we construct actions describing the particle dynamics in some of these kinematical spaces using the method of nonlinear realisations. We explain the relation with the coadjoint orbit method. We continue discussing three types of non-lorentzian gravity theories: Galilei gravity, Newton-Cartan gravity and Carroll gravity. Introducing matter, we discuss electric and magnetic non-lorentzian field theories for three different spins: spin-0, spin-1/2 and spin-1, as limits of relativistic theories.

60 pages; (v4: updated references and made minor changes. This is the final version to appear in SciPost Physics Lecture Notes.)

References in corpus (33)

• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Galilean Conformal Algebras and AdS/CFT
• Flat Holography: Aspects of the dual field theory
• Newtonian Gravity and the Bargmann Algebra
• Carroll contractions of Lorentz-invariant theories
• Dynamics of Carroll Particles
• Fractons, dipole symmetries and curved spacetime
• Expanding Lie (super)algebras through abelian semigroups
• Carroll Expansion of General Relativity
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Galilean Isometries
• Extended Galilean symmetries of non-relativistic strings
• Aspects of Nonrelativistic Strings
• Carrollian and celestial spaces at infinity
• Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity
• Limits of JT gravity
• A Non-Relativistic Limit of NS-NS Gravity
• The construction of brane and superbrane actions using non-linear realisations
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• Galilean Conformal Electrodynamics
• On the intrinsic torsion of spacetime structures
• World-Line Description of Fractons
• Galilean first-order formulation for the non-relativistic expansion of general relativity
• Schwarzian mechanics via nonlinear realizations
• N=4 superconformal mechanics as a Non linear Realization
• Generalized Newton-Cartan Geometries for Particles and Strings
• Lifshitz symmetry: Lie algebras, spacetimes and particles
• The Ashtekar-Hansen universal structure at spatial infinity is weakly pseudo-Carrollian
• Semionic Supersymmetric Solitons
• Colourful Poincaré symmetry, gravity and particle actions
• Symplectic Actions and Central Extensions