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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04522 |
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Table of 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.