Can Spontaneous Time-Translation Symmetry Breaking Be Quantized Without Explicit Branches?
Abstract
Can classically branched dynamics associated with spontaneous time-translation-symmetry breaking be quantized without explicitly retaining the branches of the Hamiltonian? We investigate this question using a reduced phase space. formulation in which the Hamiltonian is single-valued, while the critical structure of the classical Legendre map is encoded in a singular, momentum-dependent symplectic geometry. Quantization of the reduced Poisson algebra yields a deformed position-momentum commutator whose singularities determine distinct regular momentum sectors. Using the positive measure induced by the reduced symplectic structure, we identify a bounded central sector and two unbounded outer sectors. In the central sector, states with vanishing mean momentum obey a nonzero lower bound on position uncertainty, subject to the operator-domain assumptions of the representation. We further identify a possible field-theoretic connection with k-essence, where nonlinear scalar-field kinetics can produce finite-velocity degeneracies of the Legendre map. The relationship between the resulting reduced quantum description and branch-matching quantization remains unresolved and requires a comparison of the corresponding Hilbert spaces and operator domains.
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BibTeX
@misc{nandi2026spontaneous,
title = {{Can Spontaneous Time-Translation Symmetry Breaking Be Quantized Without Explicit Branches?}},
author = {Partha Nandi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32030},
eprint = {2610.32030},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32030},
}
RIS
TY - UNPB
TI - Can Spontaneous Time-Translation Symmetry Breaking Be Quantized Without Explicit Branches?
AU - Partha Nandi
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32030
UR - https://arxiv.org/abs/2610.32030
AB - Can classically branched dynamics associated with spontaneous time-translation-symmetry breaking be quantized without explicitly retaining the branches of the Hamiltonian? We investigate this question using a reduced phase space. formulation in which the Hamiltonian is single-valued, while the critical structure of the classical Legendre map is encoded in a singular, momentum-dependent symplectic geometry. Quantization of the reduced Poisson algebra yields a deformed position-momentum commutator whose singularities determine distinct regular momentum sectors. Using the positive measure induced by the reduced symplectic structure, we identify a bounded central sector and two unbounded outer sectors. In the central sector, states with vanishing mean momentum obey a nonzero lower bound on position uncertainty, subject to the operator-domain assumptions of the representation. We further identify a possible field-theoretic connection with k-essence, where nonlinear scalar-field kinetics can produce finite-velocity degeneracies of the Legendre map. The relationship between the resulting reduced quantum description and branch-matching quantization remains unresolved and requires a comparison of the corresponding Hilbert spaces and operator domains.
ER -