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Main Author: Fluxman, Jarah
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2509.04522
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author Fluxman, Jarah
author_facet Fluxman, Jarah
contents We classify the elementary classical and quantum Lifshitz systems. Lifshitz systems are systems where space and time scale anisotropically. That is, there is a constant $z$ such that under scaling by a factor of $λ$, \begin{equation*} \boldsymbol{x}\rightarrow λ\boldsymbol{x} \text{ and } t\rightarrow λ^{z}t \end{equation*} There are seven Lie groups, called the Lifshitz groups, which characterise all Lifshitz symmetries. Elementary classical Lifshitz systems are the symplectic manifolds with a transitive Lifshitz action, which turn out to be coadjoint orbits of the Lifshitz groups and their one-dimensional central extensions up to covering. Elementary quantum Lifshitz systems are the projective unitary irreducible representations of the Lifshitz groups.
format Preprint
id arxiv_https___arxiv_org_abs_2509_04522
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Elementary Classical and Quantum Lifshitz Systems
Fluxman, Jarah
High Energy Physics - Theory
Representation Theory
We classify the elementary classical and quantum Lifshitz systems. Lifshitz systems are systems where space and time scale anisotropically. That is, there is a constant $z$ such that under scaling by a factor of $λ$, \begin{equation*} \boldsymbol{x}\rightarrow λ\boldsymbol{x} \text{ and } t\rightarrow λ^{z}t \end{equation*} There are seven Lie groups, called the Lifshitz groups, which characterise all Lifshitz symmetries. Elementary classical Lifshitz systems are the symplectic manifolds with a transitive Lifshitz action, which turn out to be coadjoint orbits of the Lifshitz groups and their one-dimensional central extensions up to covering. Elementary quantum Lifshitz systems are the projective unitary irreducible representations of the Lifshitz groups.
title Elementary Classical and Quantum Lifshitz Systems
topic High Energy Physics - Theory
Representation Theory
url https://arxiv.org/abs/2509.04522