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arXiv · 2602.20968

Perturbative anomalies in quantum mechanics

Maxim Gritskov·Andrey Losev·Saveliy Timchenko
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Abstract

In this work, we propose a cohomological approach to studying perturbative anomalies in quantum mechanics. The Hamiltonian $\hat{H}$ together with the symmetry generator $\hat{S}$ forms a unitary representation of the two-dimensional Abelian Lie algebra $\mathfrak{g}\cong \mathbb{R}^{2}$ on the Hilbert space $V$. We show that perturbations of such a system are related to the first Chevalley-Eilenberg cohomology group $H^{1}_{CE}(\mathbb{R}^{2},\mathfrak{u}(V))$. In turn, the perturbative anomalies of the symmetry $\hat{S}$ are related to the second cohomology group $H^{2}_{CE}(\mathbb{R}^{2},\mathfrak{u}(V))$.

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Maxim Gritskov, Andrey Losev, Saveliy Timchenko. 2026-02-24. Perturbative anomalies in quantum mechanics. https://arxiv.org/abs/2602.20968

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