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A non-lorentzian primer
by Eric Bergshoeff, José Figueroa-O'Farrill, Joaquim Gomis
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | José Figueroa-O'Farrill |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2206.12177v3 (pdf) |
| Date accepted: | 2023-04-18 |
| Date submitted: | 2023-03-16 10:34 |
| Submitted by: | Figueroa-O'Farrill, José |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
List of changes
We have modified item (i) on page 2. Indeed the way it read did not
highlight the non-lorentzian nature. We added a new item "Carrollian
physics" separate from "flat space holography".
"Ultra-relativistic" has been replaced with "ultra-local" in three of
the four places it appeared and in the fourth case it has been removed
altogether, since it did not help the discussion.
We have clarified the notation around (4.36) and inserted the missing
\alpha in the RHS.
We have modified the discussion around equation (5.66) to explain in
what sense it is related with the field equations derived from the
action in (7.15).
Published as SciPost Phys. Lect. Notes 69 (2023)