Quantum Gravity and String Theory

(SU(m,n)) Unified Field Theory

Authors: Tomasz Kobierzycki

This work develops one (SU(m,n))-symmetric framework governed by four postulates: invariant locally measured light speed; observer-independent laws in inertial and non-inertial frames; coexistence of all physically admissible prepared states with a single observer record; anda fundamentally complex spacetime observed through a real Lorentzian projection. The fundamental arena is a pseudo-K"ahler manifold withHermitian metric and a complex four-index field equation whose trace-free sector is carried by Bochner curvature. An observer is defined by anadmissible antiholomorphic involution. Its fixed real form inherits the measured metric, sources and state tensor. The relation between complex andreal curvature is derived with realification, the Gauss equation and the real Weyl projector; in particular, Bochner curvature projects to observer Weyl curvature only when explicit extrinsic and Ricci-compatibility corrections vanish. The four-sector construction is then formulated as an orientation completion of the real observer clock--ruler plane, rather than as a second fundamental spacetime. Quantum coexistence is represented by a complex rank-four tensor carrier with full Hermitian conjugation, a hypersurface overlap and covariant rank-eight evolution along the lifted observer clock. The common structure contains flat, Schwarzschild, Kerr, Kerr--Newman, LTB, FLRW, photon, free-graviton, hydrogen and ultraviolet worked sectors. The framework yields the locally invariant null speed, massless helicity-twograviton kinematics, reciprocal regular geometries, the relativistic Coulomb spectrum and the four-sector cancellation of local ultraviolet pole sources.

Comments: 22 Pages.

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Submission history

[v1] 2026-08-22 23:39:24

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