In previous studies, the authors utilized a single-dimensional operationalization of species density that implies induction of hierarchy and time with certain topologies. For further clarification of induced fractals including the relation to renormalization in physics, here a theoretical development is proposed based on a newly identified fact, namely that scaling parameters for magnetization exactly correspond to imaginary parts of Riemann zeta nontrivial zeros. An analogy to magnetization and accompanying Fake Monster Algebra is invoked to lend support to this theory, along with empirical species density data for a wild Dictyostelia community. A master torus and a Lagrangian/Hamiltonian are derived expressing fractal structures as a solution for diminishing divergent terms in renormalization.

In This paper we introduce the integration of Renormalization Group (RG) methods with Deep Q-Networks (DQNs) to improve reinforcement learning in high-dimensional state spaces. RG methods provide multi-scale analysis, enhancing state representation, learning stability, and exploration. The proposed RG-DQN algorithm uses hierarchical Q-value estimation and multi-scale representations, demonstrating superior performance on synthetic genomic data compared to traditional DQNs.}

Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the $\lambda\phi^4$ theory in three dimensions and make a comparison between the sharp-cutoff regularization method and other more recent methods. The former gives considerably better results, while the other methods are far from optimal in the perturbative domain. In addition, these methods present theoretical problems that are already manifest in the renormalization of mass.

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton's constant and the other gravitational couplings.

The insuperable obstacle between gravity and quantum mechanics is their spacetimes. Introduction of a (quantum) quadratic form on a state Hilbert space and a (quantum) metric tensor in (3+1)D quantum spacetime solves the problem by providing a common spacetime for both gravity and quantum mechanics which helps further to develop an accurate and generalized form of quantum gravity, i.e., General Quantum Gravity. This formalism yields a (3+1)D pseudo-gravity first order quantum equation, which is technically more accurate than Schr\"odinger equation. A (quantum) Lorentz-like transformation is also possible to be developed in (3+1)D quantum spacetime. Instead of one common Einstein field equation to explain gravitational effects, this formalism yields two individual (quantum) Einstein field equations, namely, one for bosons and another for fermions. In this work, (quantum) metric tensor as well as quantum Riemann tensor, quantum Ricci tensor and quantum Ricci scalar all are found to be the objects of quantization. Apparently, these quantum Riemann tensor, quantum Ricci tensor and quantum Ricci scalar are also found to be multiplicatively renormalizable while all divergences of their higher orders vanish in (3+1)D quantum spacetime. Ultimately, General Quantum Gravity yields that: Quantum Mechanics and Theory of Special and General Relativity are inseparable and naturally inter-expressible for the (quantum) quadratic form and the (quantum) metric tensor in (3+1)D quantum spacetime.

By introducing a suitable renormalization process the charge carrier and phonon dynamics of a double-stranded helical DNA molecule is expressed in terms of an effective Hamitonian describing a linear chain, where the renormalized transfer integrals explicitly depend on the relative orientations of the Watson-Crick base pairs, and the renormalized on-site energies are related to the electronic parameters of consecutive base pairs along the helix axis, as well as to the low-frequency phonons dispersion relation. The existence of synchronized collective oscillations enhancing the π-π orbital overlapping among different base pairs is disclosed from the study of the obtained analytical dynamical equations. The role of these phonon-correlated, long-range oscillation effects on the charge transfer properties of double standed DNA homopolymers is discussed in terms of the resulting band structure.

The super-weak interaction includes three simple extensions of the standard model: gauge extension, fermionic extension, and scalar extension. All of these extensions are strongly influenced by their complex phenomenology. They can explain a number of unresolved questions in particle physics and cosmology, including the genesis of dark matter, cosmic inflation, asymmetry of matter and antimatter, neutrino masses, and vacuum stability, if combined into a single structure. This is an extension of the gauge group of the standard model $G_{\rm SM}$ by $G_{\rm SM}\otimes U(1)_Z$ without any anomalies. We investigate the implications of the development of a general Majorana mass renormalization group for neutrinos with masses in the range of 0.03 $eV$ and 0.1 $eV$, which fall within the recently published range as well as the range to be explored in future planned experiments.

The recently proposed Holography-inspired approach to quantum gravity is reviewed and expanded. The approach is based on the foliation of the background spacetime and reduction of the offshell states to the physical states. Careful attention is paid to the boundary conditions. It is noted that the outstanding problems such as the cosmological constant problem and black hole information can be tackled from the common thread of the quantized gravity. One-loop renormalization of the coupling constants and the beta function analysis are illustrated. Active galactic nuclei and gravitational waves are discussed as the potential applications of the present quantization scheme to astrophysics.

The argument of this article is threefold. First, the article argues that, from its rise in the sixteenth century to our own time, the advancement of modern physics, as mathematical-experimental science, has been defined by the invention of new mathematical structures. Secondly, the article argues that quantum theory, specifically with quantum mechanics, gave this thesis a radically new meaning by virtue of the following two features: one the one hand, quantum phenomena themselves are defined by purely physical features, as essentially different from all previous physics; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism,” RWR, interpretations. This argument allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concern only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena, in terms of probabilistic predictions, while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever discussed, apart from previous work by the present author. It will, however, be given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle.

In quantum field theory (QFT), it is well known that when Feynman diagrams containing loops are evaluated to account for self interactions, probability amplitude comes out to be infinite which is physically not admissible. So, to make the QFT convergent, various renormalization methods are conventionally followed in which an additional (infinite) counter term is postulated which neutralizes the original infinity generated by diagram. The resulting finite values of amplitudes have agreed with experiments with surprising accuracy. However, proponents of renormalization methods acknowledged that this ad-hoc procedure of subtraction of infinity from infinity to reach at a finite value is not at all satisfactory and there is no physical basis for bringing in the counter term. So, it is desirable to establish a method in QFT which does not generate any infinite term (thus not requiring renormalization), but which predicts same results as conventional methods do. In this paper, we describe such a technique taking self interaction quantum electrodynamics diagram representing electron or photon self energy. In our method, no problem of infinity arises and hence renormalization is not necessary. Still, the dependence of calculated probability amplitude on physical variables in our technique comes out to be same as conventional methods. Using similar procedure, we hope, the problem of non-renormalizability of quantum gravity may be solved in future.

This paper explores the Wilsonian renormalization group of probe-D-branes, focusing on the Dirac-Born-Infeld (DBI) action. The analysis involves deriving the constant of motion and formulating the Wilsonian renormalization group equation. The study extends to the infrared regime, considering both zero and non-zero temperatures. Additionally, thermodynamic aspects related to the functional form of the grand potential are discussed. The investigation provides insights into the renormalization of probe-D-branes and their thermodynamic properties.

Fractals and multifractals are well-known trademarks of nonlinear dynamics and classical chaos. The goal of this work is to tentatively uncover the unforeseen path from multifractals and selfsimilarity to the framework of effective field theory (EFT). An intriguing finding is that the partition function of multifractal geometry includes a signature analogous to that of gravitational interaction. Our results also suggest that multifractal geometry may offer insights into the non-renormalizable interactions presumed to develop beyond the Standard Model scale.

A Berry geometrical phase is identified in a strongly metastable system containing dynamically responsive clathrate hydrate structures within a crystal-fluid material. High energy degeneracy in the associated chemistry produces local stability and false vacuum conditions that lead to non-extensive and non-additive contributions in the fundamental thermodynamic relation. Application of Ginzburg-Landau theory and the scaling laws reveals a coherence length and a penetration depth for a macro-scale dual superconductor. The coherence length determines non-extensive volume changes whilst its inverse gives the Higgs mass. The penetration depth determines the extent of QCD vacuum suppression whilst its inverse gives the vector boson mass together with indirect manifestation as non-additive hyperbolic curvature. Simultaneous emergence of the Ginzburg-Landau superconducting phase transition is consistent with gauge-invariant coupling of the scalar field to the Yang-Mills action in QCD. The discovery of an energy gap in the gradient energy term of the system Lagrangian is associated with a critical correlation length revealed in the transition from a gapped to a gapless superconducting state. Together with the emergence and absorption of the Higgs-like scalar field, a mechanism for describing a renormalized QCD mass gap arises.

The textbook analysis of vacuum energy density (VED) in flat spacetime follows from Pauli’s lectures of 1951, in which quantum vacuum is modeled as a reservoir of free harmonic oscillators. In his lectures, Pauli shows that deriving a nearly vanishing VED is contingent upon fulfilling three corollary conditions called polynomial-in-mass-constraints. The goal of this work is to evaluate Pauli’s constraints against the Standard Model parameters and the Higgs mechanism of spontaneous symmetry breaking.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.