The Coherent State Projection Eigenvalue Theorem
Abstract
Recent papers have developed a cyclic symmetry projected extension for coherent state representations of bosonic Hilbert space. This extension can greatly reduce sampling errors in phase-space simulations of bosonic quantum systems that have symmetries. Here we prove an eigenvalue theorem for the continuum limit of the projected coherent states. Our intuitively appealing result is that in the continuum limit the projected coherent states are eigenstates of the symmetry generating operator. This result gives a differential identity in phase-space that includes the conserved eigenvalues. Detailed applications of these differential identities to obtaining improved Fokker-Planck and stochastic equations in many-body physics will be given elsewhere.
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BibTeX
@misc{drummond2026coherent,
title = {{The Coherent State Projection Eigenvalue Theorem}},
author = {Peter D. Drummond and Margaret D. Reid},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33613},
eprint = {2610.33613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33613},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Coherent State Projection Eigenvalue Theorem
AU - Peter D. Drummond
AU - Margaret D. Reid
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33613
UR - https://arxiv.org/abs/2610.33613
AB - Recent papers have developed a cyclic symmetry projected extension for coherent state representations of bosonic Hilbert space. This extension can greatly reduce sampling errors in phase-space simulations of bosonic quantum systems that have symmetries. Here we prove an eigenvalue theorem for the continuum limit of the projected coherent states. Our intuitively appealing result is that in the continuum limit the projected coherent states are eigenstates of the symmetry generating operator. This result gives a differential identity in phase-space that includes the conserved eigenvalues. Detailed applications of these differential identities to obtaining improved Fokker-Planck and stochastic equations in many-body physics will be given elsewhere.
ER -