Can Spontaneous Time-Translation Symmetry Breaking Be Quantized Without Explicit Branches?

Partha Nandi

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arXiv · 2610.32030

Can Spontaneous Time-Translation Symmetry Breaking Be Quantized Without Explicit Branches?

Partha Nandi

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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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Partha Nandi. 2026-10-23. Can Spontaneous Time-Translation Symmetry Breaking Be Quantized Without Explicit Branches?. https://arxiv.org/abs/2610.32030

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