A non-lorentzian primer

Bergshoeff, Eric; Figueroa-O'Farrill, José; Gomis, Joaquim

doi:10.21468/SciPostPhysLectNotes.69

SciPost Physics Lecture Notes

A non-lorentzian primer

Eric Bergshoeff, José Figueroa-O'Farrill, Joaquim Gomis

SciPost Phys. Lect. Notes 69 (2023) · published 31 May 2023

doi: 10.21468/SciPostPhysLectNotes.69
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysLectNotes.69
TI  - A non-lorentzian primer
PY  - 2023/05/31
UR  - https://www.scipost.org/SciPostPhysLectNotes.69
JF  - SciPost Physics Lecture Notes
JA  - SciPost Phys. Lect. Notes
SP  - 69
A1  - Bergshoeff, Eric
AU  - Figueroa-O'Farrill, José
AU  - Gomis, Joaquim
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysLectNotes.69,
	title={{A non-lorentzian primer}},
	author={Eric Bergshoeff and José Figueroa-O'Farrill and Joaquim Gomis},
	journal={SciPost Phys. Lect. Notes},
	pages={69},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysLectNotes.69},
	url={https://scipost.org/10.21468/SciPostPhysLectNotes.69},
}

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Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.

¹ Eric Bergshoeff,
² José Figueroa-O'Farrill,
³ Joaquim Gomis

Funders for the research work leading to this publication

Ministerio de Ciencia, Innovación y Universidades
Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])