Quantum and Classical mechanics vs QFT

TL;DR

This paper explores how quantum mechanics and classical physics emerge from a pre-geometric quantum field theory framework by introducing Planck constants as elements of an emergent metric, highlighting phase transitions that connect these regimes.

Contribution

It extends the Akama-Diakonov-Wetterich theory by incorporating Planck constants into the emergent metric, proposing a mechanism for the emergence of quantum mechanics from pre-geometric quantum fields.

Findings

Quantum mechanics emerges via symmetry breaking or emergent symmetry mechanisms.

The inverse Planck constant acts as an order parameter for phase transitions.

Path integral formulation of QM arises from the QFT phase in the model.

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 $\hbar\omega$, 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 $1/\hbar \rightarrow 0$, and the area of classical physics (CM) in the limit $\hbar \rightarrow 0$. 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 $1/\hbar \rightarrow \infty$.