Perturbative anomalies in quantum mechanics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910038710288384 |
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| author | Gritskov, Maxim Losev, Andrey Timchenko, Saveliy |
| author_facet | Gritskov, Maxim Losev, Andrey Timchenko, Saveliy |
| contents | 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 $H^{2}_{CE}(\mathbb{R}^{2},\mathfrak{u}(V))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20968 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perturbative anomalies in quantum mechanics Gritskov, Maxim Losev, Andrey Timchenko, Saveliy Mathematical Physics High Energy Physics - Theory 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 $H^{2}_{CE}(\mathbb{R}^{2},\mathfrak{u}(V))$. |
| title | Perturbative anomalies in quantum mechanics |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.20968 |