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The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) isdescribed in detail. CCGG emerges naturally in the Palatini formulation, wherethe vierbein and the spin connection are independent fields. Neither torsionnor non-metricity are excluded. The manifestly covariant gauge process is basedon canonical transformations in the De Donder-Weyl Hamiltonian formalism,starting from a small number of basic postulates. Thereby, the original systemof matter fields in flat spacetime, represented by non-degenerate Hamiltoniandensities, is amended by spacetime fields. The coupling of matter and spacetimefields leaves the action integral of the combined system invariant under activelocal Lorentz transformations and passive diffeomorphisms, aka Principle ofGeneral Relativity. We consider the Klein-Gordon, Maxwell-Proca, and Diracfields and derive the corresponding equations of motion. Albeit the coupling ofthe given matter fields to the gauge fields are unambiguously determined byCCGG, the dynamics of the free gauge fields must be postulated based onphysical reasoning. Our choice allows to derive Poisson-like equations ofmotion also for curvature and torsion. The latter is proven to be totallyanti-symmetric. The affine connection is a function of the spin connection andvierbein fields. Requesting the spin connection to be anti-symmetric givesnaturally metric compatibility. The canonical equations combine to an extensionof the Einstein-Hilbert action with a quadratic Riemann-Cartan concomitant thatendows spacetime with inertia. Moreover, a non-degenerate, quadratic version ofthe free Dirac Lagrangian is deployed. When coupled to gravity, the Diracequation is endowed with an emergent mass parameter, a curvature-dependent masscorrection, and novel interactions between particle spin and spacetime torsion.

Covariant Canonical Gauge Theory of Classical Gravitation for Scalar, Vector, and Spin-1/2 Particle Fields