Quantum Gravity and String Theory

Matrix-Based Approach to the Quantization of Spacetime Via Modified Dirac Spinor Metrics

Authors: Michael Heilmann

In this paper, an 8x8 tensorial metric is constructed—using both the 4x4 Dirac matrices and their corresponding temporal and spatial 2x2 Pauli components—to serve as a scalar substitute for the standard single-component dimensions; the resulting field equation is intended to be basis-invariant and consistent with General Relativity. This is achieved without abandoning or inconsistently altering the smooth Minkowski metric of the Dirac equation; instead, the inertial frame determined by the Dirac matrices—along with the aforementioned 8x8 metric—is maintained alongside the spacetime-curved inertial frame. Following the evaluation and characterization of this specific metric, temporal-energetic and spatial-momentum separations—as well as their hybrid interrelationships—are established; these are then systematically developed into a field equation for quantum gravity using factors, wave functions, Lorentz gamma factors, temporal and spatial derivatives, and their corresponding operators and tensors. The author now presents this universal equation of quantum mechanics for appropriate discussion and falsification.

Comments: 30 Pages. In German

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Submission history

[v1] 2026-09-28 20:41:11

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