Quantum GTG-DC NONPERTURBATIVE_PUBLICATION: A Coframe-Based Quantum Theory of Gravity — From the Quantum Physical Sector to Classical GTG-DC, Gravitational Waves, RAR, and BTFR
Year: 2026
Type: preprint
Abstract: This manuscript presents a developed nonperturbative construction of Q-GTG within an explicitly specified effective-field-theory domain. The term “nonperturbative” refers primarily to the way the theory is defined: its fundamental action, state structure, and mutual coupling between the different sectors are not constructed as an expansion in small field amplitudes. Perturbative expansion appears only subsequently, after a particular reference solution has been selected, and serves as a controlled limit of the theory rather than as its defining starting point. The formalism can therefore describe finite-amplitude states and nonlinear response while remaining an effective theory with a stated range of energies, momenta, and resolution. The central physical idea of Q-GTG is to treat geometry, source, and the internal state of the system as mutually coupled components of a single dynamical structure. The source is not merely an external current inserted into an already fixed linear field equation. It can modify the internal state of the system; that state can in turn modify the geometric response; and the modified response can feed back onto the source and its subsequent evolution. The problem is therefore not reduced to calculating a field generated by matter specified once and for all, but instead takes the form of a self-consistent source–field–state system. In the galactic sector this also means that the spatial matter distribution, environment, boundary conditions, three-dimensional geometry, and preparation history are parts of the physical problem rather than corrections added after the field has already been solved. The geometric core of the theory is formulated using a coframe and a single physical metric. The manuscript separates physical degrees of freedom from redundancies associated with coordinate choice and local Lorentz frames, and it consistently takes into account the fact that changing the geometry may also change the state, selectors, spatial operators, and boundary data. The variational problem is therefore not restricted to local equations of motion but also includes operator domains and boundary contributions. This becomes particularly important whenever the source, detector, or energy flux is associated with a boundary. The geometric framework is not automatically identified with a complete strong-field solution or with a globally unique time direction; those issues are explicitly left as separate problems. A major component of the construction is the convex “root” sector, which possesses an exact dual structure and allows specific reductions to be performed without expansion in small amplitudes. The manuscript analyzes its uniqueness properties, stability, behavior near zero, and consequences for numerical calculations. Particular care is taken to distinguish the internal root variable used in the effective action from the physical root measure appearing in other parts of the Q-GTG program. The two are not declared identical merely because they play related roles or carry similar terminology. The absence of a fully derived microscopic bridge between these descriptions remains one of the principal open questions. A second characteristic element is the finite Bloch sector. Its state space is compact and possesses its own symplectic structure, allowing the dynamics to remain on the correct orbit without artificially projecting the system back onto the constraint surface after every evolution step. The manuscript discusses both the classical geometry of this space and the conditions for its quantization, its local oscillator representation, and the exact finite-amplitude solution of the homogeneous block. At the same time, the full Bloch orbit and its local tangent-oscillator description are not counted as two independent physical sectors. This is part of a broader single-counting principle for degrees of freedom, introduced to prevent artificial duplication of the physical state space. The geometry, root, Bloch, formation, and relational-transfer sectors are set out explicitly in the opening part of the manuscript. Q-GTG also contains a formation sector and a relational mechanism of state transfer. Formation describes the process by which the state evolves along a selected time direction, while transfer is represented by a graph-based structure and depends primarily on relations between nodes rather than on an absolute value attached to a single variable. The time direction is not treated as an entirely arbitrary external input: the manuscript analyzes its relation to the state of the system, the regularity requirements of the corresponding selector, and the problems that arise near degeneracies. The complete transfer functions are not, however, presented as already derived microscopically across the entire amplitude range. Their absolute normalization and deeper origin remain subjects for further work. A distinct dynamical sector is provided by an explicit reservoir. It allows memory, delayed response, dissipation, and fluctuations to be represented in a causal manner rather than by introducing phenomenological friction independently of the microscopic origin of the noise. Once the reservoir is integrated out, its effects appear as response and correlation kernels. The manuscript examines the spectral representation, passivity, power balance, and stability conditions, while clearly distinguishing an explicitly retained reservoir from the equivalent influence-functional description. These are again alternative representations of the same physical content rather than two independent systems. The reservoir, memory, closed-time-path formalism, and the 1PI and 2PI functionals form a central part of the mathematical machinery of the publication. The quantum structure is organized through the theory of constraints and the BRST/BV formalism. This allows physical degrees of freedom to be separated from gauge redundancies and establishes conditions that physical observables must satisfy. The manuscript also discusses the role of the measure, possible anomalies, and the BFV boundary structure. An important distinction is maintained between local satisfaction of classical symmetry relations and the complete global quantum problem. The local BRST/BV architecture belongs to the constructed framework, whereas a global quantum measure, complete gluing of all coordinate patches, control of all topologies, and the fully global quantum master equation are not presented as completed results. Nonequilibrium dynamics are organized by the closed time path. The two contour branches do not represent two physical copies of matter; they are a calculational structure used to obtain real causal response and state evolution. On this basis the manuscript develops the 1PI and 2PI functionals and the Dyson–Schwinger hierarchy. Because that hierarchy is formally infinite, merely writing it down is not identified with solving the theory. A controlled closure must specify which correlations, couplings, and symmetry relations are retained. That role is played by the C-SPR1 closure. It keeps the lowest nonzero level of the relevant 2PI skeleton structures together with the required mixed vertices, contact terms, ghosts, and counterterms. Unknown microscopic functions are not replaced by arbitrarily chosen polynomials merely to obtain a desired result. Of particular importance is the full mixed response between coupled sectors: the physical response is not obtained by solving independent propagators and subsequently adding a correction, but by solving the coupled response problem. Self-consistency also includes the dependence of correlations on the current mean field. C-SPR1 is therefore more than a single perturbative correction, while at the same time it is not presented as an exact resummation of the entire infinite hierarchy. In the computational part, the theory is formulated as a common fixed-point problem for the fields, internal state, correlations, and — where its dynamics have been specified — the source itself. The NPQ12 archive contains numerical evidence concerning convergence, constraint preservation, the Dyson equation, full block response, and energy balance. The manuscript carefully qualifies the status of this evidence: the archived numerical values were checked against the preserved source material, but the complete historical NPQ12 solver was not rerun from first principles for the present edition. These results are therefore treated as archived evidence for the behavior of the specific closure, rather than as a new independent numerical experiment. The manuscript also separates numerical precision from the correctness of the operator itself: a very small numerical residual for an incorrectly specified operator is not evidence that the underlying theory is physically correct. The manuscript further studies the physical state space, energy forms, lower-boundedness requirements, and the regulator limit. Local stability and stability of finite regulated approximations are not automatically promoted to a theorem about the entire theory in the continuum limit. Likewise, convergence of a particular eigenvalue or solution is not treated as proof of convergence of all correlation functions. A complete result would require compatible embeddings of state spaces together with control of the measure, operators, state, and regulator. This distinction is one of the key differences between a solved nonperturbative subsystem and a complete microscopic quantum theory. Another major part of the work concerns the spectrum. The publication stresses that not every propagator pole must correspond to a new physical particle: poles may arise from gauge degrees of freedom, auxiliary variables, constraints, or an incorrect reduction. The physical spectrum must therefore be read from the correlators of properly reduced observables. On a regular frozen branch, the source material allows the standard transverse-traceless ten
Author: Mróz, Maciej
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225632694
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