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arXiv · 2607.16029

Quantum Mechanics on Lie Groups: II. Path Integrals

Mathieu Beauvillain·Blagoje Oblak·Marios Petropoulos
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Abstract

We continue our study of quantum dynamics on a Lie group $G$, initiated in arXiv:2512.19840, by building the path integral that governs transition amplitudes in the Hilbert space $L^2(G)$. This relies on the proper handling of both a noncommutative momentum space and the presence of compact directions in $G$. We show that compactness can be handled through a sum over winding numbers in maximal tori of $G$, generalizing the similar sum commonly encountered for path integrals on a circle. As applications, we compute semiclassical approximations of propagators and partition functions of Euler-Arnold systems, up to (and including) two-loop order.

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Mathieu Beauvillain, Blagoje Oblak, Marios Petropoulos. 2026-07-17. Quantum Mechanics on Lie Groups: II. Path Integrals. https://arxiv.org/abs/2607.16029

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