arXiv:2602.21243v1 Announce Type: new
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 $hbaromega$, 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 $1/hbar rightarrow infty$.