arXiv subjects

Sadataka Furui

Publications and source records attributed to Sadataka Furui.

At least 19 recordsLinked to original sources

arXiv2024

Analysis of $(3+1)D$ and $(2+1)D$ nonlinear ultrasonic waves using conformal invariance

Localization and classification of scattered nonlinear ultrasonic signatures in 2 dimensional complex damaged media using Time Reversal based Nonlinear Elastic Wave Spectroscopy (TR-NEWS) approach is extended to 3 dimensional complex damaged media. In (2+1)D, i.e. space 2 dimensional time 1 dimensional spacetime, we used quaternion bases for analyses, while in (3+1)D, we use biquaternion bases. The optimal weight function of the path of ultrasonic wave in (3+1)D lattice is obtained by using the Echo State Network (ESN) which is a Machine Learning technique. The hysteresis effect is incorporated by using the Preisach-Mayergoyz model. We analyze the spectrum data of Wire Arc Additive Manufacturing (WAAM) sample obtained by Quaternion Excitation Symmetry Analysis Method (QESAM) using the conformally invariant quantum mechanical variables of de Alfaro-Fubini-Furlan and their supersymmetrically extended variables of Fubini-Rabinovici.

physics.optics↗

arXiv2024

Biquaternion Signal Processing for Nonlinear Ultrasonics

physics.optics↗

arXiv2024

The optimization of paths in the $R^{3,1}$ space time by Markov Chain Monte Carlos

We propose a method to obtain the optimal weight function of 9 paths in (3+1)D space-time whose length is less than or equal to $2\times (6+2)$ lattice units. The factor 2 comes from inclusion of opposite direction path or time reversed paths. There are $2\times 2$ time shifts, which we assume that they can be regarded as stochastic Markov processes. We prepare the input 9D vector ${\bf X}$ and a $9\times 9$ matrix ${\bf W}$ and a bias vector ${\bf b}$, and consider affine transformations ${\bf Z}^{(h)}={\bf X}^{(in)}{\bf W}^{(h)T}+{\bf b}^{(h)}$ and ${\bf A}^{(h)}=\sigma({\bf Z}^{(h)})$ from an input layer to a hidden layer, the hidden layer to another hidden layer and from the hidden layer to an output layer, using the transformation ${\bf Z}^{(x)}={\bf A}^{(h)}{\bf W}^{(out) T} +{\bf b}^{(x)}$ and ${\bf A}^{(x)}=\sigma({\bf Z}^{(x)})$. By choosing the matrix ${\bf W}$ a diagonal matrix, and introducing the information of action of the 9 paths, a simple Monte Carlo simulation yields actions on a 2D plane spanned by $e_1, e_2$ for a fixed $u_2=j_2 e_2$ as a function of $u_1=j_1 e_1$. The action at high momentum region has small fluctuations, but at small momentum region, has large fluctuation. Generalizing $\bf W$ including mixing of paths, we search the optimal weight function using the Machine Learning (ML) techniques. For fixed point actions, actions of the output layer are defined by the output of final hidden layer

hep-lat↗

arXiv2023

On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$

We study application of the Clifford algebra and the Grassmann algebra to image recognitions in $(3+1)D$ using quaternions. Following S.L.Adler, we construct a quaternion-valued wave function model with fermions and bosons of equal degrees of freedom, similar to Cartan's supersymmetric model. The Clifford algebra ${\mathcal A}_{3,1}$ is compared with ${\mathcal A}_{2,1}$ and the model applied to the $(2+1)D$ non-destructive testing is extended. The fixed point lattice actions are calculated for 7 paths in $(3+1)D$ space with lengths less than or equal to 8 lattice units. Comparison with the quaternion time approach of Ariel, quaternion Fourier transform of Hitzer and the tensor renormalization group approach to classical lattice models are also discussed.

math-ph↗

arXiv2022

Clifford Fourier Transforms in (2+1)D Lattice Simulations of Soliton Propagations

Monte Carlo simulation of solitonic phonon propagation on a 2D plane in Weyl fermion-sea is analyzed. We assume materials are filled with Weyl spinors located on $256\times 256$ 2D lattice points, which are expressed by quaternions ${\bf H}$. The topology of solitonic phonon propagation is defined by modifying fixed point actions of 4D Quantum Chromo Dynamics action to (2+1)D action, replacing Dirac fermions by Weyl fermions, and changing the electric charge current flow to the energy flow. We consider $A$ type loops whose path are on a 2D plane, and $B$ type loops which contain two parallel links that connect two 2D plane on different time slices. The length of loops are restricted to be less than or equal to 8 lattice units. At the moment spatial lattice unit and time lattice unit are same. They can be chosen arbitrarily when one compares hysteresis effects with experimental data. Using the quaternion expression of Porteous, we calculate the plaquette part of loop actions and the link part of loop actions. Link actions of $A$ type loops cancel with each other, but those of $B$ type loops depends on whether the spin rotation is clockwise or that is counterclockwise. In the present work we consider average of clockwise rotating and counterclockwise rotating loop contributions.

hep-lat↗

arXiv2022

Analysis of Phonetic Soliton Propagation in Neutral Weyl Fermion-sea

We propose application of Machine Learning (ML) and Neural Network (NN) technique for the analysis of ultrasonic Time Reversal based Nonlinear Elastic Wave Spectroscopy (TR-NEWS). In order to acquire topological features, we adopt the $(2+1)D$ lattice simulation with fixed point (FP) actions. We consider 7 A type loops which sit on $2D$ spacial plane spanned by $e_1, e_2$ and 13 B type loops which contain links parallel to $e_1\wedge e_2$ and to -$e_1\wedge e_2$. We consider propagation of bosonic phonons in Fermi-sea of neutral Weyl spinors which are described by Clifford algebra. Configurations in momentum space is transformed to real position space via Clifford Fourier Transform. We consider A-type without hysteresis effects and B-type with hysteresis effects, and via ML or NN technique search optimal weight of 7 A-type FP actions and 13 B-type FP actions using the Monte-Carlo method.

physics.gen-ph↗

arXiv2021

Monte Carlo simulations of phonon propagation in the Fermi-sea of Weyl spinors and detection of hysteresis effects using Groupoids

We considered symplectic quaternions sitting on a $(2+1)D$ lattice in momentum space which interact with nearest neighbor interactions. The action is expressed by fixed point actions given by the superposition of blocks whose length of the contour is 4, 6 or 8 lattice spacings. The spinors are on a finite $2D$ plane expressed as $u_1 a e_1+ u_2 a e_2$ (A type) and/or on two $2D$ planes separated by $\pm a e_1\wedge e_2$ (B type). In the A type, link actions on counter-clockwise rotating loop and on clockwise rotating loop cancel, however in the B type, the direction of links between the lower $2D$ plane and the upper $2D$ plane induces differences in the action. The time-reversal conserving and spin rotational symmetry breaking actions can be measured. Result of Monte-Carlo simulations of $64\times 64$, $128\times 128$ and $256\times 256$ spatial lattices are presented.

hep-lat↗

arXiv2021

Renormalization of $(2+1)D$ scalar Weyl spinors interactions on lattices using the Clifford groups

We consider symplectic quaternions instead of unitary spinors sitting on a lattice, and calculate the fixed point Wilson action on a finite $2D$ plane expanded by $u_1 a e_1+ u_2 a e_2$ and on two $2D$ planes separated by $a e_1\wedge e_2$. Only the nearlest neighbor interactions are considered. Following Migdal and Kadanoff, we perform the renormalization of the Wilson action by making the lattice spacing $(\frac{1}{2})^{h}a$ $(h=0,\cdots,11 )$, in order to simulate bosonic and solitonic phonon propagation in materials. Renormalization group method of Benfatto and Gallavotti for $(2+1)D$ scalar $\phi^4$ system for sound propagation in Fermi sea is applied and feasibility of numerical simulation is discussed.

hep-lat↗

arXiv2021

Lattice simulation of $(2+1)D$ phonetic solitons and the Renormalization group

The outline of lattice simulations of $(2+1)D$ soliton-propagations in the background of Weyl spinors is presented. Clifford algebra is applied on Luescher's domain decomposition method. The Clifford algebra shows that there are loop parts and interpolating surface parts in the Wilson's lattice action. We adopt the Migdal-Kadanoff prescription and the fixed point action in momentum space of Benfatto and Gallavotti, and shows a road map for simulating phonetic solitons in materials. Detections of topological anomalies (APS index) in nondestructive testing are discussed.

hep-lat↗

arXiv2021

A Closer Look at Gluons

Gluons are strong interaction gauge fields which interact between quarks, i.e. constituents of baryons and mesons. Interaction of matters is phenomenologically described by gauge theory of strong, electromagnetic, weak and gravitational interactions. In electro-weak theory, left handed leptons ${l}_L$ and neutrino ${\mathcal \nu}_L$, right handed leptons ${l}_R$ and left handed quarks $u_L, d_L$ and right handed quarks $u_R, d_R$ follow $SU(2)\times U(1)$ symmetry. Charge of leptons and quarks define hypercharge $Y$, and via Higgs mechanism $SU(2)_L\times U(1)_Y$ symmetry forms $U(1)_{em}$ symmetry. In order to describe Hadron dynamics properly, embedding of 4-dimensional space to 5-dimensional space was tried in lattice simulations, and in light front holographic QCD (LFHQCD) approach in which conformally symmetric light-front dynamics without ghost are embedded in $AdS_5$, and a parameter that fixes a mass scale was chosen from the Principle of Maximum Conformality. Coulomb or Landau gauge fixed Faddeev-Popov Yang-Mills field equation is known to have the Gribov ambiguity, and tunneling between vacua between different topological structures was proposed by van Baal and collaborators. The symmetry of three colors can be assigned three vectors of quaternion ${\bf H}$, whose multiplication on $2\times 2$ matrices of Dirac spinors on ${\bf S}^3$ induces transformations. Instantons or sphalerons whose presence is expected from conformal equivalence of ${\bf S}^3\times {\bf R}$ to ${\bf R}^4$ are reviewed. An extension of the dynamics embedded in complex projective space is also discussed.

physics.gen-ph↗

arXiv2021

Understanding Quaternions from Modern Algebra and Theoretical Physics

Quaternions were appeared through Lagrangian formulation of mechanics in Symplectic vector space. Its general form was obtained from the Clifford algebra, and Frobenius' theorem, which says that "the only finite-dimensional real division algebra are the real field ${\bf R}$, the complex field ${\bf C}$ and the algebra ${\bf H}$ of quaternions" was derived. They appear also through Hamilton formulation of mechanics, as elements of rotation groups in the symplectic vector spaces. Quaternions were used in the solution of 4-dimensional Dirac equation in QED, and also in solutions of Yang-Mills equation in QCD as elements of noncommutative geometry. We present how quaternions are formulated in Clifford Algebra, how it is used in explaining rotation group in symplectic vector space and parallel transformation in holonomic dynamics. When a dynamical system has hysteresis, pre-symplectic manifolds and nonholonomic dynamics appear. Quaternions represent rotation of 3-dimensional sphere ${\bf S}^3$. Artin's generalized quaternions and Rohlin-Pontryagin's embedding of quaternions on 4-dimensional manifolds, and Kodaira's embedding of quaternions on ${\bf S}^1\times {\bf S}^3$ manifolds are also discussed.

physics.gen-ph↗

arXiv2020

Application of Quaternion Neural Network to Time Reversal Based Nonlinear Elastic Wave Spectroscopy

Identification of crack positions or anomalies in materials using the time reversal based nonlinear elastic wave spectroscopy (TR-NEWS) is an established method. We propose a system using transducers which emit forward propagating solitonic wave and time-reversed propagating solitonic wave produced by memristers placed on a side of a rectangle and scattered by cracks in the material and received by receivers which are placed on the opposite side of the rectangle. By minimizing the difference of the scattered forward propagating wave and the scattered TR wave, we get information of the position of the crack by using the neural network technique. Route of the solitons are expressed by 2 dimensional projective quaternion functions, and parameters for getting the optimal route from signals are expected to be reduced. We consider the wave is expressed by a soliton which is conformal, and discuss symmetry protected topological impurities and gravitational effects using the Atiyah-Patodi-Singer's index theorem.

physics.gen-ph↗

arXiv2020

Supersymmetry in Hadron Spectroscopy and Solitons in 2 Dimensional Fermionic Media

An overview of hadron spectroscopy obtained from an extension of superconformal field theory of de Alfaro, Fubini and Furlan, which originates from the supergauge transformation of Wess and Zumino and influenced on the string theory are preseted. The standard model of hadron dynamics is based on gauge theory. In the 4 dimensional ($4D$) QCD Lagrangian, the Faddeev-Popov ghost that appears to compensate unphysical degrees of freedom in internal fermion propagators can be regarded as the partner of a fermion. Donaldson formulated a $5D$ gauge theory. Fubini and Rabinovici formulated superconformal quantum mechanics in de Sitter space, and Brodsky and de Téramond formulated relativistic light front holographic QCD (LFHQCD) in Kaluza-Klein type $5D$ anti de Sitter (AdS) space, using Dirac's light cone gauge, and succeeded in obtaining spectroscopy of baryons (fermions) and corresponding mesons (bosons), except the pion which is an axial scalar meson that remains massless. In the LFHQCD, the time parameter $τ=t\pm z/c$, $(z\in {\bf C})$ appears by the choice of the light-cone gauge, or the front form of Dirac's formulation. The theory is an extension of AdS/CFT correspodence of Maldacena in which incorporation of Einstein's gravity theory in Maxwell's electromagnetic theory was tried in the framework of the string theory. Taking mathematical frameworks of treating the supersymmetry by Brodsky, Witten, Connes and their collaborators as central thema, we summarize other supersymmetric approaches like string theory in particle physics and astrophysics. We discuss about 2 dimensional solitons whose dynamics is represented also by $τ=t\pm z/c$, ($z\in$ pure quaternion${\bf H}$).

hep-th↗

arXiv2016

Cartan's Supersymmetry and the Decay of a $h^0$ with the mass $m_{h^0}\simeq 11$GeV to $Υ(1S)γ$ and to $Υ(nS)γ(n=1,2,3)$

In the LHCb detector at CERN, decays of $χ_b(3P)$ meson to $Υ(1S)γ$ and $Υ(2S)γ$ are reported at centre-of-mass energy of $\sqrt s=7$ and 8 TeV. Following the success of the assignment of $χ_b(1P)\toΥ(1S)γ$ of the mass of $m(χ_b(1P))=9.8923$ GeV and $χ_b(2P)\toΥ(1S)γ$ of the mass of $m(χ_b(2P))=10.2547$ GeV, the new state $χ_b(3P)$ of the mass of 10.5157 GeV was assigned, but its $J^{P}$ was not fixed. We study the possibility that this boson is the light Higgs boson $h^0(0^+)$, and study its decay modes to a $b\bar b$ which reduces to an $Υ(mS)$ ($m=1,2$ or 3) and $\bar q q$ which reduces to a $γ$, using the Cartan's supersymmetry. Recent non observation of polarizations of $Υ(nS)$ by the CMS collaboration is consistent with the theory.

hep-ph↗

arXiv2016

Cartan's Supersymmetry and the Decay of a $H^0(0^+)$

We compare the decay of a Higgs boson $H^0(0^+)\to\ell\bar\ell \ell\bar\ell\toγγ$, $H^0(0^+)\to W\bar W\to \ell\barν\bar\ellν$, and $H^0(0^+)\to Z\bar Z\to\ell\bar\ell\ell\bar\ell$ using Cartan's supersymmetry, that defines coupling of a vector particle $x_i$ and Dirac spinors $ψ$ and $ϕ$. Apparent discrepancy of $H^0(0^+)\toγγ/\ell\bar\ell \ell\bar\ell$ experimental data of ATLAS and CMS collaborations disappears, since the sum of transition to $\ell\bar\ell \ell\bar\ell$ and $γγ$ have the meaning. The trilinearity of leptons vector fields coupling and the initial wave functions to be large components define Higgs-leptons couplings. The ratio of Higgs boson decay branching ratios $H\to WW=21.6\pm 0.9$, $H\toγγ=0.228\pm 0.011$ can be reproduced when we multiply coupling constant $α_s\simeq 1$ for $WW$ and $α_e=1/137$ for $γγ$ to the number of independent diagrams. Comparison with Atiyah-Witten's quark-gluon dynamics on a manifold of $G_2$ holonomy theory is added.

hep-ph↗

arXiv2016

Cartan's Supersymmetry and the violation of CP symmetry

Cartan's supersymmetriy fixes couplings of two types of fermions $ψ, ϕ$ and two types of vector fields $x_i$ and $x_{i'}$, ($i=1,2,3,4$). The electromagnetic interaction of leptons and quarks is expressed as ${^tψ}{\mathcal C}x_iψ$. In the case of coupling of leptons and quarks with $W$, we extend the coupling ${^tϕ}{\mathcal C}Xψ$ to ${^tϕ}{\mathcal C}X(1-γ_5)ψ$, where $X=x_i$ or ${x_i}'$, and unify the interactions in the form $ {^tϕ}{\mathcal C}\bar{x_i}ψ+{^tϕ}{\mathcal C} \bar{{x_i}'} {\mathcal C}ψ$, where $\bar{x_i}$ implies appropriate $x_i$ or $(-γ_5 x_i)$ is chosen. The $γ_5$ term induces in time component of $B^0\to K^0\, J/Ψ$, $K^0$ with the $\bar s$ quark dominated by the small component, while in space components of $\bar B^0\to \bar K^0\, J/Ψ$, $\bar K^0$ with the $s$ quark dominated by the small component. This asymmetry could be the origin of the $CP$ asymmetry in the $B^0\to K^0\, J/Ψ$. We apply the model to $B_{s(d)}^0\to D_{s(d)}^- D_{s(d)}^+$ decays and study violation of $CP$ symmetry via interference of tree and penguin contributions, and observe that the asymmetry is weak consistent to the experiment.

physics.gen-ph↗

arXiv2015

Departure from the Standard Model of Meson Decays and Cartan's Supersymmetry

The experimental decay branching ratios of mesons like $B_s\to \ell\bar \ell$ and $B_d\to \ell\bar \ell$ ($\ell=e$ or $μ$) do not agree completely with the standard model (SM). Cartan's supersymmetry predicts relation of the coupling of vector particles $x_μ, x_μ'$, ($μ=1,2,3,4$) to Dirac spinors of large components $ψ, ϕ$ and small components $\mathcal Cψ, \mathcal Cϕ$. In the decay of $B_d=\bar b d$, the Cabibbo-Kobayashi-Maskawa(CKM) model suggests that the contribution of $t$ quark dominates, while in the decay of $B_s=\bar b s$, contribution of $c$ quark in the intermediate state is expected to be large, since $s$ and $c$ quark belong to the same CKM sector. The relative strength of the $t$ quark and $c$ quark contribution in Cartan's supersymmetric model has more freedom than that of the SM. Together with the problem of enhancement of $B_d\to J/ΨK_0$ in high $Δt$ region, we can understand the problem of branching ratios of $B$ decay into $e\bar e$ and $μ\barμ$, if the Nature follows Cartan's supersymmetry.

physics.gen-ph↗

arXiv2015

Cartan's Supersymmetry and Weak and Electromagnetic Interactions

We apply the Cartan's supersymmetric model to the weak interaction of hadrons. The electromagnetic currents are transformed by $G_{12},G_{123},G_{13},G_{132}$ and the factor$(1-γ_5)$ is inserted between $l \barν$ or $\bar l ν$ when the photon is replaced by $W^\pm$, and between $l \bar l$ or $ν\bar ν$ when the photon is replaced by $Z$. Electromagnetic currents in the Higgs boson $H^0$ decay into 2$γ$ and $D_s(0^+)$ decay into $D_s(0^-)π$ and $D_s(0^-)γ$ in which leptons are replaced by quarks are also studied. A possibility that the boson near the $B\bar B$ theshold $χ_b(3P, 10.53$ GeV) is the Higgs boson partner $h^0$ is discussed. We adopt Dirac lepton neutrinos and Majorana quark neutrinos, and construct a model that satisfy the $Z_3$ symmetry of the lepton sector and the quark sector, by adding two right-handed neutrinos whose left-handed partner cannot be detected by our electro-magnetic detectors.

hep-ph↗