Quantum Mechanics on Lie Groups: II. Path Integrals

2026/07/17 by Mathieu Beauvillain, Blagoje Oblak, Marios Petropoulos
#quant-ph #hep-th #math-ph #math.CA #math.MP

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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 L²(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.

Citations

• Techniques and Applications of Path Integration
• Curvatures of left invariant metrics on lie groups

Cited by

• Quantum Mechanics on Lie Groups: I. Noncommutative Fourier Transforms

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