Quantum GTG-DC: A Coframe-Based Quantum Theory of Gravity — From the Quantum Physical Sector to Classical GTG-DC, Gravitational Waves, RAR, and BTFR

Abstract

Quantum GTG-DC is a coframe-based quantum theory of gravity constructed on the geometric foundation of classical GTG-DC, published in the Zenodo record https://zenodo.org/records/21872403. The present record develops its quantum branch: the action of the theory, its gauge structure, physical Hilbert space, quantum carrier of gravity, interaction amplitudes, gravitational waves, and the causal transition to the classical field response. The mathematical framework presented here derives the effective classical version of GTG-DC from its quantum-physical formulation on the regular prepared branch of the theory. In this construction, classical gravity is not the starting point of quantization but a controlled limit of the quantum theory. The derivation begins with the quantum dynamics of the coframe field. It then proceeds through BRST/BV gauge reduction, construction of the physical state space, identification of the propagating degrees of freedom, pole and residue analysis, LSZ reduction, helicity amplitudes, and perturbative unitarity tests. Through coherent states and the causal closed-time-path formalism, the construction continues to a classical gravitational wave and an effective classical field-response system. In this precisely delimited sense, classical GTG-DC is not merely an independent model appended to the quantum formalism. Its effective weak-field dynamics emerges as a classical limit of the quantum construction presented here. After the full nonspherical three-dimensional response has been obtained, and after explicitly defined conditions are imposed—including the selected constitutive transmission law, isolation, radial symmetry, regularity, and appropriate boundary conditions—the same mechanism reduces successively to a two-potential AQUAL-like system, the radial acceleration relation, a MOND-like dynamical limit, and the baryonic Tully–Fisher relation. AQUAL, RAR, the MOND-like limit, and BTFR are therefore not independent phenomenological laws appended to the theory. They are successive conditional reductions of the same mathematical construction. The complete mechanism forms a single coherent chain: quantum coframe action⟶ gauge structure and BRST/BV reduction⟶ physical Hilbert space Hphys⟶ physical TT sector with helicities λ=+2,−2⟶ poles, residues, and LSZ reduction⟶ amplitudes and scattering channels⟶ Ward/ST, crossing, and unitarity tests⟶ coherent states and classical gravitational waves⟶ causal CTP quantum-to-classical limit⟶ effective classical GTG-DC⟶ full nonspherical three-dimensional response⟶transmission law, isolation, radial symmetry,regularity, and boundary conditionstwo-potential AQUAL-like system⟶ radial RAR⟶ MOND-like limit⟶ BTFR. The most characteristic property of the theory is the continuity of this chain. Its quantum part does not end with a formal propagator, a spectrum of states, or a selected set of amplitudes. At the same time, its galactic description does not begin by postulating an empirical interpolation law. The two domains are connected through the construction of the physical state space, the transition to coherent states, the closed-time-path functional, the causal classical limit, and the full three-dimensional field equations. Quantum GTG-DC therefore does not end with a formal quantum spectrum and scattering amplitudes. On its regular prepared branch, it recovers effective classical GTG-DC and subsequently—after explicit reduction conditions have been imposed—leads to AQUAL, the radial RAR, a MOND-like limit, and BTFR. The physical quantum sector After gauge reduction, the regular massless physical sector contains two transverse-traceless states with helicities λ=+2,λ=−2. These are the opposite helicity states of one physical carrier of gravity. They do not represent positive- and negative-energy particles, nor do they constitute two distinct particle species. The GTG-DC carrier is identified neither with the photon nor with the graviton postulated in the perturbative quantization of General Relativity. It is a new, not yet empirically identified quantum of the physical GTG-DC sector. Its properties follow from the action, constraints, gauge symmetries, and state space of this theory rather than from transferring the properties of another field. The effective spectrum also contains a separate gapped scalar-like Bloch quasistate characterized by the scale ΩB. It is not a third polarization of the massless carrier. It constitutes a distinct effective sector whose pole, threshold, and possible observational signatures require independent identification. The physical character and internal consistency of the regular perturbative sector are investigated through: BRST cohomology and construction of the physical state space; pole positions and residue signs; LSZ reduction; Ward and Slavnov–Taylor identities; helicity amplitudes; crossing relations; partial-wave decompositions; explicit unitarity cuts; infrared-sector control; subtraction of the long-range asymptotic phase; independent symbolic and numerical checks. These tests form an interconnected internal consistency network. The same degrees of freedom must survive gauge reduction, possess admissible physical residues, generate mutually compatible crossed channels, and satisfy the available perturbative unitarity relations. From a carrier quantum to a gravitational wave A gravitational wave has a direct state-based interpretation in quantum GTG-DC. A single excitation of the physical TT sector is one quantum of the carrier, while a classical wave corresponds to a coherent state containing many such quanta. The wave-field operator can be expanded in the basis of physical polarizations: HijTT(x)=λ=±2∑∫(2π)32ωkd3k[ϵij(λ)(k)aλ(k)e−ik⋅x+ϵij(λ)∗(k)aλ†(k)eik⋅x]. The state aλ†(k)∣0⟩ describes one quantum of the physical carrier with helicity λ. The classical wave field is obtained as the expectation value of the field operator in a coherent state: Hij,clTT(x)=⟨α∣HijTT(x)∣α⟩. On the regular weak-field radiative branch, the quantum field is mapped to the dimensionless physical strain tensor: σijTT=κg,RHijTT,κg,R2=32πG, in units c=ℏ=1. The massless pole of the TT sector corresponds to propagation on the physical cone. A conserved tensor source generates a wave with a leading quadrupolar character. The wave field produces tidal curvature, changes the relative separation of freely falling test systems, and leads to a physical interferometric readout. The resulting chain is carrier quantum⟶many-quantum state⟶coherent state⟶classical wave field⟶tidal curvature⟶detector signal. The accompanying wave monograph also investigates source coupling, multipolar emission, propagation, energy flux, worldline couplings, Schur/Fokker reduction, radiation reaction, the CTP formalism, wave memory, and interferometric signal readout. The TT sector, its two helicities, the massless pole, the coherent-state construction, and the normalization of the weak-field readout belong to the regular perturbative branch. Complete strong-field closure for compact objects and a unique determination of all dynamical vector and shift channels remain open elements of the theory. The causal transition to classical GTG-DC The classical limit is not introduced merely by formally replacing quantum operators with classical fields. It is constructed using the closed-time-path functional, which preserves the causal structure of the response and accommodates a prepared macroscopic state, retarded response, memory, and environmental influence. In the appropriate ℏ→0 limit, the effective functional leads to a classical parent system containing: the total-source channel; the target-source channel; nonlinear transmission; a memory variable; a compensating response; environmental contributions; the physical matter readout within the specified weak-field realization. The result is not immediately a radial algebraic relation, but a full nonspherical three-dimensional system. This distinction is essential because a general geometry contains a solenoidal field that cannot be discarded without additional assumptions concerning symmetry, topology, and boundary behavior. Within this scope, the quantum framework recovers the effective classical dynamics of GTG-DC. This does not yet constitute a global derivation of all its strong-field, cosmological, and nonperturbative branches. From the full 3D response to AQUAL, RAR, MOND, and BTFR In the isolated local sector, the three-dimensional system reduces to an exact two-potential AQUAL-like system. The standard one-potential AQUAL form requires an additional identification and is not a universal identity of the full three-dimensional theory. The selected constitutive transmission law is Θ(y)=1−exp(−y),y=a0gN. Only after radial symmetry, isolation, regularity, and conditions eliminating the additional solenoidal flux have been imposed does one obtain the closed relation g=1−exp[−gN/a0]gN. In the low-acceleration limit, g2≃a0gN. For the exterior region of a finite baryonic mass, gN(r)=r2GMb, and, after imposing the circular-motion condition, rvc2=g, one obtains the asymptotic baryonic Tully–Fisher relation vf4=GMba0. The galactic laws therefore appear at the end of the derivation rather than at its beginning. If isolation, radial symmetry, regularity, or the relevant boundary conditions are not satisfied, one must return to the full three-dimensional system. The radial RAR is not a universal local substitute for the parent field equations. Scope and character of the theory The construction combines within one mathematical framework several domains that are usually investigated separately: a quantum coframe action; gauge symmetries and the BRST/BV formalism; construction of the physical Hilbert space; identification of a physical carrier with helicities +2 and −2; analysis of an additional gapped sector; scattering amplitudes and perturbative unit