Simplicial quantum dynamics

TL;DR

This paper proposes a novel approach to quantum field theory using simplicial decompositions, leading to a regularized, finite-dimensional framework that alters fundamental principles like the uncertainty principle and offers new insights into quantum gravity.

Contribution

It introduces a simplicial quantization method that replaces traditional infinite-dimensional spaces with high-dimensional spinor spaces, providing a new perspective on quantum dynamics and gravity.

Findings

Replaces infinite-dimensional Hilbert spaces with finite-dimensional spinor spaces.

Reformulates gauge bosons and gravity as bound fermion pairs.

Suggests a new regularization scheme altering the uncertainty principle at small scales.

Abstract

Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups. It radically changes the uncertainty principle for small distances. Gaugeons, including the gravitational, are represented as bound fermion-pairs, and space-time curvature as a singular organized limit of quantum non-commutativity. Keywords: Quantum logic, quantum set theory, quantum gravity, quantum topology, simplicial quantization.