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Open Quantum Systems Decoherence
Quantum Simulation
Discrete Action, Graph Evolution, and the Hierarchy of Symmetries: A Rigorous Construction of Temporal Layers C1 → C2 → C3 → C4
arXiv
Authors: Medeu Abishev, Daulet Berkimbayev
Year
2025
Paper ID
16761
Status
Preprint
Abstract Read
~2 min
Abstract Words
137
Citations
N/A
Abstract
Postulating a minimal discrete quantum of action S=hbar and a simple rule for the growth of an oriented graph, we construct a strict hierarchy of temporal layers C N with discrete periods τN=Nhbar/E. Each layer is specified by its configuration space, symplectic structure, update rule, and emergent symmetry. At C1 the state is represented by a single oriented edge with U(1) phase ei E t/hbar. The transition C1 → C2 splits the edge into two independent flows, which yields canonical pairs \(xa,pa\), local U(1) invariance, and an effective (2{+}1) metric with signature (+--). The closure C2 → C3 produces SU(3) connections and an Einstein-Yang-Mills type action. We show that these structures follow from discrete-action principles, and that stochastic graph growth naturally provides mechanisms for decoherence and spontaneous symmetry breaking.
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- Postulating a minimal discrete quantum of action S=hbar and a simple rule for the growth of an oriented graph, we construct a strict hierarchy of temporal layers C N with...
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