2025/09/03 by Jarah Fluxman, Fluxman, Jarah
Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum optics and atomic interactions #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2509.04522
openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, \boldsymbolx→ λ\boldsymbolx and t→ λzt 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.