Coherent States and Quantum Geometry Phenomenology

H. Bacry, Alex Grossmann, J. Žák

Julian Schwinger

Borros Arneth

Quantum mechanics is traditionally formulated on complex Hilbert spaces, while geometry is usually introduced only after the quantum formalism has been established. In this work, we investigate an alternative viewpoint in which a coherence manifold constitutes the fundamental object and Hilbert space emerges as a derived structure. Local quantum dynamics are described by a complex coherence coordinate W= Omega + iTheta, where Omega represents radial coherence and Theta represents holonomy phase. The wavefunction arises naturally as phi=exp(Omega+iTheta), and the continuity equation, quantum Hamilton–Jacobi equation, and Schrödinger equation emerge from the differential geometry of the coherence manifold. We further propose that the discrete quadruples (a,b,c,d), originally introduced in the Triple-Coherence framework, should be interpreted as coherence quantum numbers rather than phenomenological fitting parameters. This leads naturally to a coherence operator whose spectrum is determined by a rank-four coherence lattice. The resulting framework combines ideas from geometric quantum mechanics, geometric quantization, spectral geometry, fiber-bundle theory, and representation theory within a common geometric language. We argue that elementary particles may be interpreted as stable eigenstates of coherence geometry and that the observed particle spectrum may represent a subset of a larger coherence spectrum.

James Thomas Wheeler

Borros Arneth

Quantum mechanics is traditionally formulated on complex Hilbert spaces, while geometric structures are introduced only after the quantum formalism has been established. In this work, we investigate a coherence-geometric reformulation in which geometry is fundamental and Hilbert space emerges as a derived structure. The framework is based on a coherence manifold with local coordinates , where denotes radial coherence and denotes holonomy phase. The wavefunction arises naturally as , and the continuity equation, quantum Hamilton–Jacobi equation, and Schrödinger equation emerge from the differential geometry of the coherence manifold. A second ingredient is a discrete coherence spectrum characterized by quadruples . These integers are interpreted as coherence quantum numbers rather than phenomenological fitting parameters. The resulting framework introduces a coherence operator whose spectrum is determined by a rank-four coherence lattice. We further propose a Coherence Resonance Condition in which stable particle states correspond to rational phase locking between local coherence oscillations and global holonomy cycles. The framework combines concepts from geometric quantum mechanics, geometric quantization, Berry holonomies, Yang–Mills gauge theory, spectral geometry, and representation theory within a common geometric language.

Clinton Svancara

This work presents a phenomenological, RFT-inspired coherence model for entanglement stability in open quantum systems. A scalar quantity R_c(t)is introduced as a coarse-grained descriptor of phase-aligned correlation structure, motivated by off-diagonal density-matrix coherence but not intended to replace standard measures such as concurrence, negativity, or entanglement entropy. The model proposes a first-order dynamical equation balancing effective decoherence against interaction-driven coherence restoration. Numerical experiments in controlled classical fields are used as structural analogues, not direct quantum simulations. These experiments show that coherence-like behavior can separate into gradient-based intensity components and structure-tensor components that respond differently to shear- and vortex-dominated geometries. The results support a multi-component view of coherence in which stability may depend not only on scalar magnitude but also on geometric organization. The framework is exploratory and phenomenological, intended to motivate future comparison with full Lindblad/open-system simulations and experimental quantum platforms.