Quantum Mechanics on Lie Groups: II. Path Integrals
Mathieu Beauvillain, Blagoje Oblak, Marios Petropoulos
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.
Create a lesson
Related papers
Single-Particle Spectral Estimation
Adrian Chapman, Charles Derby, Steven T. Flammia et al.
Learning SYK Hamiltonians
Anurag Anshu, Srinivasan Arunachalam, Sitan Chen et al.
From Permutation Symmetry to Communication Bounds and Additivity
Zahra Baghali Khanian, Debbie Leung, Graeme Smith
Robust exponential lower bounds for fermionic and bosonic Gaussian ranks
Fuchuan Wei, Kong-Wing Wu, Zhengwei Liu et al.
Polynomial-time classical and quantum simulation of quantum impurity models
Jiaqing Jiang, Nathan Ju, Ojas Parekh et al.
Beyond Light Cones: State Preparation Complexity in Quantum Spin Glasses
Omar Al-Ghattas, David Gamarnik, Bobak T Kiani