Part X -Extended Fractal-Hue Field Theory: A Broad Framework

2025

This paper explores the recursive renormalization group (RG) flows in higher-spin AdS/CFT, investigating the emergence of fractal universality classes through trigonometric and modular invariance. By examining twistor monodromy and epicycloidal quantization, we also explore their impact on gravitational wave echoes and neutrino mass hierarchies. Additionally, we integrate quantum roulette dynamics in dark matter halos and baryogenesis, presenting a unified theory governed by trigonometric-cycloidal symmetry. The results provide predictions for upcoming experimental tests of the framework, including LIGO, DUNE, and JWST experiments. We present a reformulation of recursive fractal spacetime dynamics within the framework of renormalization group (RG) flow in higher-spin holography. By recasting recursive convergence points (RCPs) as generalized fixed-point structures in AdS/CFT, we establish a direct link between multi-scale corrections to gravitational dynamics and asymptotic safety scenarios in extended gauge sectors. We demonstrate that higher-order monodromies in twistor geometry provide a natural mathematical framework for describing cycloidal influence structures, which manifest as nontrivial winding modes contributing to modular symmetries in holographic entanglement entropy.

In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatial section runs from 1.5 to 3, and under particular assumptions from 2 to 3 across a 1.5 phase when the energy of a probe scalar field decreases from high to low energy in a fictitious time T . We calculated also the spectral dimension of space-time using the scaling of the area spectrum operator calculated on spin-foam models. The main result is that the effective dimension is 2 at the Planck scale and 4 at low energy. This result is consistent with two other approaches to non perturbative quantum gravity: causal dynamical triangulation and asymptotically safe quantum gravity. We studied the scaling properties of all the possible curvature invariants and we have shown that the singularity problem seems to be solved in the covariant formulation of quantum gravity in terms of spin-foam models. For a particular form of the scaling (or for a particular area operator spectrum) all the curvature invariants are regular also in the Trans-Planckian regime.

We study the large source asymptotics of the generating functional in quantum field theory using the holographic renormalization group, and draw comparisons with the asymptotics of the Hopf characteristic function in fractal geometry. Based on the asymptotic behavior, we find a correspondence relating the Weyl anomaly and the fractal dimension of the Euclidean path integral measure. We are led to propose an equivalence between the logarithmic ultraviolet divergence of the Shannon entropy of this measure and the integrated Weyl anomaly, reminiscent of a known relation between logarithmic divergences of entanglement entropy and a central charge. It follows that the information dimension associated with the Euclidean path integral measure satisfies a c-theorem.

2025

This paper presents a comprehensive framework integrating recursive expansive dynamics, p-adic quantum geometry, adelic number theory, hyperfolding rings, and golden-ratio modulated recursive structures. We derive a new action principle that unifies quantum gravity, cosmology, and algebraic geometry through recursive Lie algebra deformations, recursive entropy scaling, and adelic corrections to gauge theories. Key results include: (i) The Inverse Zero Operator (IZO) as a renormalization tool, stabilizing infinities in gravitational entropy. (ii) Recursive entropy corrections explaining black hole microstates and gravitational wave echoes. (iii) Adelic Gromov-Witten invariants linking p-adic geometry with quantum field theory. (iv) Fractal p-adic correspondence showing that Hausdorff-dimension-modulated structures naturally emerge from adelic cohomology. (v) ϕ-modulated gravitational delays testable in LIGO-Virgo, with predictions for log-periodic cosmological modulations. We explore implications for quantum holography, number-theoretic quantum gravity, and nonlocal field theories, establishing testable predictions and a mathematically rigorous extension of QFT and gravity.

The journal is devoted primarily to the integration of nonlinear dynamics, deterministic chaos and fractals into the very foundation of quantum and high energy physics. In addition we encourage papers dealing with completely novel and partially abstract mathematical theories and techniques in solving fundamental problems in theoretical physics. The journal will accept papers in noncommutative geometry, K-theory, transfinite and intuitionistic set theory, descriptive set theory, number theory, fractal spacetime theories, E-infinity theory, fractal tiling, quantum gravity via fractal Regge calculus, knot theory, wild topology, Euclidean Nash embedding, Lie symmetry groups, fuzzy set theory and fuzzy physics, exotic manifolds in physics, fractal Yang-Mills theories, loop quantum gravity, super string theories, n-categories, E-infinity rings and E-infinity algebra applied to physics, fractal cosmological models, chaotic inflation theories, dark matter and dark energy models, applications of nonlinear dynamics in nano and quantum technologies, advanced experimental techniques in fundamental quantum physics, measurement and quantum paradoxes, fiber bundles and fractal gauge theory, foliation and symplectic geometry in physics. The Editorial Board will intermittingly invite and commission special issues on timely and novel developments in quantum physics and related mathematical subjects.

Physics Letters B, 1998

We compute the intrinsic Hausdorff dimension of spacetime at the infrared fixed point of the quantum conformal factor in 4D gravity. The fractal dimension is defined by the appropriate covariant diffusion equation in four dimensions and is determined by the coefficient of the Gauss-Bonnet term in the trace anomaly to be generally greater than 4. In addition to being testable in simplicial simulations, this scaling behavior suggests a physical mechanism for the screening of the effective cosmological 'constant' and inverse Newtonian coupling at very large distance scales, which has implications for the dark matter content and large scale structure of the universe.

International Journal of Modern Nonlinear Theory and Application, 2013

At its most basic level physics starts with space-time topology and geometry. On the other hand topology's and geometry's simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.

In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical structure of quantum field theory with particular reference to the processes of non-equilibrium symmetry breaking. The functional realization of fractals in terms of the q-deformed algebra of coherent states is also presented. From one side, this sheds some light on the dynamical formation of fractals. From the other side, it also exhibits the fractal nature of coherent states, thus opening new perspectives in the analysis of those phenomena where coherent states play a relevant role. The global nature of fractals appears to emerge from local deformation processes and fractal properties are incorporated in the framework of the theory of entire analytical functions.

Propagators for charged fermions no longer follow the prescription of perturbative quantum field theory in the deep infrared (IR) and ultraviolet (UV) sectors of particle physics. They acquire a fractal structure from radiative corrections contributed by gauge bosons. Here we show how fractal propagators in QFT may be analyzed using fractional field theory on space-times having minimal deviations from four-dimensionality (4 D  ,  << 1). An intriguing consequence of this approach is the emergence of classical gravity as long-range and ultra-weak excitation of the Higgs condensate.

Rodolfo Pitti, 2025

In this paper, I present an innovative theoretical framework that unites quantum mechanics, fractal geometry, and information dynamics to investigate exotic matter states and adaptive systems across multiple scales. My approach centers on scale-dependent equations incorporating fractal-dimensional scaling, denoted as (Df−d)(D_f - d)(D_f - d) , which I propose as a unifying principle governing diverse phenomena, including quantum phase transitions, supersolid properties, neural plasticity, and information processing. A key focus of my analysis is quantum neuroplasticity, where I argue that synaptic dynamics exhibit quantum-like coherence and multi-scale adaptability. Through this lens, I explore how fractal scaling and quantum effects could underpin the brain’s remarkable learning capabilities, extending classical neuroscience into a quantum-inspired paradigm. I further detail the framework’s potential applications in quantum computing, neuromorphic engineering, and biological information systems, offering robust experimental strategies—such as quantum state tomography and multi-scale neural recording—to test my hypotheses. Additionally, I reflect on the philosophical implications, suggesting that consciousness might emerge as a quantum-like informational process influenced by fractal structures. This work challenges conventional boundaries between physics, biology, and information theory, providing a novel synthesis with transformative potential. I invite further investigation through empirical validation and interdisciplinary collaboration to refine and expand these ideas, bridging quantum theory with complex adaptive systems.