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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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| _version_ | 1866918159934554112 |
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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 |