Unified Field Theory Based on Four-Dimensional Spacetime Density Tensor(IV): Canonical Quantization of Continuous Fields

Based on the Einstein-Cartan (EC) geometric framework and the monistic ontology of the spacetime density tensor, the first three papers of this series have realized the classical global unification of gravity, electromagnetism, Bohmian quantum dynamics, SU (2) weak interaction and SU (3) strong interaction hehl1976general. Relevant achievements include the geometric generation of gauge symmetries, causal self-consistency of quantum entanglement, geometric interpretation of core phenomena of strong and weak interactions, and verification of gradual theoretical degeneration. A complete unified field theory requires a self-consistent quantum dynamical foundation. Traditional quantization of continuous gravity is plagued by ultraviolet divergence and non-renormalizability, which stem from the assumption of infinite divisibility of spacetime geometry and the dimensional mismatch of the gravitational coupling constant weinberg1995quantum. Loop quantum gravity achieves ultraviolet cutoff via spacetime discretization at the cost of breaking four-dimensional continuous symmetry and Lorentz invariance rovelli2004quantum. String/M-theory relies on higher-dimensional manifolds and supersymmetry hypotheses, making it incompatible with the four-dimensional intrinsic classical unified system. Strictly following all postulates, geometric definitions, perturbation decomposition paradigms and coupling parameter systems proposed in previous papers, this paper carries out canonical quantization of the four-dimensional continuous field for the spacetime density tensor field. With the adoption of the ADM 3+1 spacetime decomposition arnowitt1962dynamics and Dirac constraint quantization scheme dirac1964lectures, we construct the complete classical canonical system, Poisson bracket structure, quantum commutation relations and constraint equations for physical states. Supported by the upper limit of saturated density of the spacetime medium and the intrinsic minimum effective action scale, a geometrically originated and dynamically self-consistent ultraviolet cutoff mechanism is established. While fully preserving the four-dimensional continuous manifold, Lorentz symmetry and all gauge symmetries, this mechanism fundamentally eliminates divergent quantum fluctuations at short distances and thoroughly resolves the non-renormalizability problem of continuous gravity. The quantization system is fully consistent with the classical five-force unification framework presented in the preceding papers. Gravitational curvature perturbations, electromagnetic shear perturbations, global Bohmian quantum coherence perturbations bohm1952suggested, weak chiral torsion perturbations and strong color topological perturbations are all upgraded into quantum field operators. The hierarchical quantum dynamics of orbital entanglement and spin entanglement are completely retained. Gradual limit tests indicate that the theory reduces to standard quantum field theory and Bohmian quantum dynamics in the low-energy weak-field regime, while quantum divergences are naturally suppressed by the intrinsic properties of the spacetime medium in the Planck-scale high-energy regime. This work completes the quantum closure of the series theory and establishes an integrated unified field foundation combining classical global unification and self-consistent quantization of continuous fields. Distinct from mainstream quantum gravity paradigms, it features fully reproducible mathematical structures, well-defined theoretical boundaries and extensive prospects for further research. It can support follow-up studies including quantum correction, quantum coupling of gauge fields, quantum effects of black holes, phenomenological research on the early universe, and numerical simulation of multi-particle entanglement.