English

A non-lorentzian primer

High Energy Physics - Theory 2023-05-31 v4 General Relativity and Quantum Cosmology Differential Geometry

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.

Keywords

Cite

@article{arxiv.2206.12177,
  title  = {A non-lorentzian primer},
  author = {Eric Bergshoeff and José Figueroa-O'Farrill and Joaquim Gomis},
  journal= {arXiv preprint arXiv:2206.12177},
  year   = {2023}
}

Comments

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

R2 v1 2026-06-24T12:02:52.030Z