[论文解读] Quantum and Classical mechanics vs QFT

G. E. Volovik|arXiv (Cornell University)|Feb 14, 2026

Noncommutative and Quantum Gravity Theories被引用 0

一句话总结

本论文通过将 Planck 常数视为新出现的度量元素，扩展 Akama-Diakonov-Wetterich 理论，概述了从前几何量子场论到量子力学再到经典力学的路径，并讨论了量子力学如何作为对称性破缺的一个相出现。

ABSTRACT

15 years ago Dmitry Diakonov wrote the paper "Towards lattice-regularized Quantum Gravity", arXiv:1109.0091. In his approach, gravity with metric and tetrads arise from pre-geometric quantum fields leading to unusual dimensions of physical quantities. In particular, particle masses are dimensionless. We are trying to extend the Akama-Diakonov-Wetterich theory by introducing the Planck constants $\hbar$ and ${/\!\!h}=\hbar c$ as elements of the emergent metric. The inverse Planck constant $1/\hbar$ has the dimension of frequency, and, therefore, the mass $M$ of a particle, which has the dimension $\hbarω$, is dimensionless. In this extension, quantum mechanics emerges from the intrinsic quantum fields either in the symmetry breaking mechanism (GUT), or in the opposite mechanism of emergent symmetry in the low-energy corner (anti-GUT). In both cases, quantum mechanics (QM) serves as a bridge between the area of quantum fields (QFT) in the limit $1/\hbar ightarrow 0$, and the area of classical physics (CM) in the limit $\hbar ightarrow 0$. In the GUT scheme the inverse Planck constants, $1/\hbar$ and $1/{\\!\!h}$, play the role of the order parameter of the symmetry breaking phase transition from the pre-geometric QFT state to the QM state, in which the quantum mechanics emerges together with the space-time metric. In this phase transition, the integration over field variables in the QFT phase transforms to a path integral formulation of QM, which in turn yields the laws of classical mechanics in the limit $1/\hbar ightarrow \infty$.

研究动机与目标

• Motivate the extension of ADW theory to include Planck constants as metric elements and explore the resulting phase structure between QFT, QM, and CM.
• Describe how inverse Planck constants act as order parameters for symmetry breaking from a pre-geometric QFT state to a quantum-mechanical state.
• Propose a normalization and dimensional framework where Planck constants define emergent spacetime quantities and mass dimensions become dimensionless.
• Investigate the implications for cosmological constant, UV scales, and the emergence of tetrads and metric in the QM phase.

提出的方法

• Introduce GUT and anti-GUT perspectives within ADW theory and their relation to emergent tetrads and metric.
• Formulate the extended ADW action with Planck constants as components of the emergent Minkowski metric (Eq. 7).
• Use normalized units to recast fields and action (Eq. 9–10) and derive the dimensionless masses and Planck-scale relations.
• Discuss how the phase transition from QFT to QM is governed by 1/ħ and 1/ħ̄, acting as order parameters for symmetry breaking.
• Relate this framework to Wilczek-type pre-geometric models and examine wavefunction, correlations, and entropy considerations across phases.

实验结果

研究问题

• RQ1 How can Planck constants be incorporated as elements of the emergent metric in ADW-type theories?
• RQ2 What is the role of inverse Planck constants as order parameters for symmetry breaking from pre-geometric QFT to QM?
• RQ3 How does the QM phase lead to emergent tetrads and a Minkowski metric with normalized units?
• RQ4 What are the implications for masses, cosmological constant, and UV scales in the extended framework?
• RQ5 How do correlations and thermodynamics of the pre-geometric vacuum influence wavefunction collapse and the QFT→QM→CM transition?

主要发现

• Planck constants can be treated as metric elements in the emergent Minkowski spacetime (Eq. 7).
• Inverse Planck constants act as order parameters for symmetry breaking from a pre-geometric QFT to a QM state, with 1/ħ = 0 in the symmetric phase.
• In the QM phase, masses become dimensionless and re-expressed via a Planck-scale normalization, tying mass to the Planck mass M_P=1 in certain units (Eq. 11).
• A unimodular emergent gravity scenario with constant tetrad determinant E is obtained when ħ and ħ̄ are nonzero, linking E to ħ via E = -1/ħ^4 (Eq. 8).
• The framework connects QFT, QM, and CM through phase transitions, with suggested links to thermodynamics of the vacuum and potential resolutions to cosmological constant issues.
• The work discusses extended symmetry groups and fermion generations (N_F=4) as natural in the pre-geometric approach and their implications for dark matter and beyond.