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Sadataka Furui

Publications and source records attributed to Sadataka Furui.

At least 37 records · Page 2Linked to original sources

Triality selection rules of Octonion and Quantum Mechanics

We apply the Cartan's supersymmetric model to the electromagnetic and weak interaction of leptons and hadrons, and study dynamics of $π^0,η,η'$ meson and Higgs boson. We adopt the Clifford algebra, express Pauli spinors by quaternions, Dirac spinors by octonions, and take into account the supersymmetric transformations $G_{ij}$ and $G_{ijk}$ of Cartan. When Higgs boson is assigned as Cartan's spinor pairs $Ψ=\barψψ$ or $Φ=\barϕϕ$, its decay into $γγγγ$ does not occur, but there appear 8 diagrams of $Ψ\toγγ$ and 8 diagrams of $Φ\toγγ$. If our world matter makes 4.6\% of the total matter, and we can interpret the matter transformed by $G_{23},G_{12},G_{123},G_{13}, G_{132}$ or about 5 times of our matter, i.e. 23\% corresponds to dark matter. We can assign the world transformed by $G_{12}, G_{123}, G_{13}$ and $G_{132}$, which make about 2/3 of the total corresponds to the dark energy. Experimentally, 72\% of the total matter corresponds to dark energy.

hep-ph↗

On the amplitude of External Perturbation and the Chaos via Devil's Staircase -Stability of Attractors -

We made the chaotic circuit proposed by Chua and the memristic circuit proposed by Muthuswamy and Chua, and analyzed the behavior of the voltage of the capacitor, electric current in the inductor and the voltage of the memristor by adding an external sinusoidal oscillation ${\dot y}(t)\simeq {\dot i_L}(t)$ of a type $γω\cosωt$, while the ${\dot x}(t)\simeq {\dot v_C}(t)$ is given by $y(t)/C$, and studied the Devil's staircase route to chaos. We compared the frequency of the driving oscillation $f_s$ and the frequency of the response $f_d$ in the window and assigned $W=f_s/f_d$ to each window. When capacitor $C=1.0$, we observe stable attractors of Farey sequences $\displaystyle W=\{\frac{1}{2}, \frac{2}{3},\frac{3}{4},\frac{4}{5}, \cdots ,\frac{14}{15},\frac{1}{1}\}$, which can be interpreted as hidden attractors, while when $C=1.2$, we observe unstable attractors. Possible role of octonions in quantum mechanics and Cartan's supersymmetry is discussed.

nlin.CD↗

On the Amplitude of External Perurbation and Chaos via Devil's Staircasein Muthuswamy-Chua System

We recently analyzed the voltage of the memristic circuit proposed by Muthuswamy and Chua by adding an external sinusoidal oscillation $γω\cosωt$ to the ${\dot y}(t)\simeq {\dot i_L}(t)$, when the ${\dot x}(t)\simeq {\dot v_C}(t)$ is given by $y(t)/C$. When $f_s<f_d$ we have observed that the Hölder exponent of the system with $C=1$ is larger than 1, and that of the system with $C=1.2$ is less than 1. The latter system is unstable, and the route to chaos via the devil's staircase is observed. Above the mode of $f_d=1, f_s=1$ observed at $ω\simeq 0.5$, we observed a mode of $f_d=1, f_s=2$ at $ω\simeq 1.15$ and $\simeq 1.05$, in the case of $C=1$ and 1.2, respectively, and a mode of $f_d=2, f_s=3$ at $ω\simeq 0.85$ and $\simeq 0.78$, in the case of $C=1$ and 1.2, respectively. At high frequency of $f_s$, there is no qualitative difference in the stability of the oscillation for $C=1$ and $C=1.2$

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Axial anomaly and the triality symmetry of leptons and hadrons

We apply the supersymmetric model of É. Cartan to the pseudoscalar meson decay into two photons, $π_0\toγγ$, $η\toγγ$ and $η'\toγγ$. In the book of É. Cartan published in 1966, Dirac spinors ${^t(}A,B)$ and ${^t(}C,D)$ and vector fields $E$ and $E'$ were introduced and five supersymmetric transformations $G_{23}, G_{12}, G_{13}, G_{123}$ and $G_{132}$ were considered. The Pauli spinor is treated as a quaternion and the Dirac spinor is treated as an octonion. In the pseudoscalar meson decay, when the two final vector fields belong to the same group ($EE$ or $E'E'$), we call the diagram rescattering diagram. When they belong to different groups ($EE'$), the diagram is called twisted diagram. Assuming the triality selection rules of octonions, dark matter is interpreted as matter emitting photons in a different triality sector than that of electromagnetic probes in our world.

hep-ph↗

Axial anomaly and the triality symmetry of octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion makes an octonion, and the gauge field can be treated as self-dual, we calculate the axial current and two vector currents triangle diagram of Bardeen, which yields the contribution of the axial anomaly. The octonion possesses the triality symmetry, and there are 5 symmetry operations $G_{ij}$ and $G_{ijk}$ ($ijk=123)$, in which mixing of spinors and vectors occur. $G_{23}$ does not mix vectors and spinors, but mismatch of the spinor and vector fields occurs. Hence, electro magnetic (EM) wave emitted from galaxies transformed by the five transformations would not be detected by EM detectors in our galaxy, and the source would be regarded as dark matter. The axial anomaly appears as a reflection of the symmetry of the matter field and not as a reflection of the symmetry of the pure vacuum, which is consistent with recent arguments on condensates and confinement.

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The flavor symmetry in the standard model and the triality symmetry

A Dirac fermion is expressed by a 4 component spinor which is a combination of two quaternions and which can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic vector fields. The triality symmetry relates three sets of spinors and two sets of vectors, which are transformed among themselves via transformations $G_{23}, G_{12}, G_{13}$, $G_{123}$ and $G_{132}$. If the electromagnetic (EM) interaction is sensitive to the triality symmetry, i.e. EM probe selects one triality sector, EM signals from the 5 transformed world would not be detected, and be treated as the dark matter. According to an astrophysical measurement, the ratio of the dark to ordinary matter in the universe as a whole is almost exactly 5. We expect quarks are insensitive to the triality, and triality will appear as three times larger flavor degrees of freedom in the lattice simulation.

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The magnetic mass of transverse gluon, the B-meson weak decay vertex and the triality symmetry of octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass $m_{mag}$ becomes approximately equal to $T_c$ at $T=T_c\sim 1.14Λ_{\bar{MS}}\sim 260$MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.

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Fermion flavors in quaternion basis and infrared QCD

I analyze the lattice simulation data of the Domain Wall Fermion in quaternion basis. As pointed out by Atiyah and Ward, the minimum action solution for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via Penrose twistor transform, to algebraic bundles on the complex projective 3-space. Assuming dominance of correlation between the fermions on the domain walls via exchange of instantons, I extract parameters necessary for defining gauge fields of Atiyah-Ward ansatz. The QCD effective coupling in the infrared and the relation between the number of flavors and the infrared fixed point is investigated. Consequence of this lepton flavor assignment to phenomenology of baryons is also discussed.

hep-ph↗

Domain Wall Fermion Lattice Simulation in Quaternion Basis

In the QCD analysis, when quarks are expressed in quaternion basis, the quark and its charge conjugate together are expressed by octonions and the octonion posesses the triality symmetry. Gluos are expressed by Plücker coordinates of spinors. Roles of triality in the proton charge form factor, three loop gluon self energy, technicolor, fine tuning and unparticle physics are discussed.

hep-ph↗

On the roles of triality in the infrared QCD

In the QCD analysis, when quarks are expressed in quaternion basis, the product of quaternions are expressed by octonions and the octonion posesses the triality symmetry. Roles of triality in the gluon self energy calculation and finite temperature QCD is explained.

hep-ph↗

Infrared fixed point of QCD, critical flavor number and triality automorphism of octonions

We show that the discrepancy on the critical flavor number of fermions $N_f^c$ for the appearance of the infrared fixed point based on the t'Hooft anomaly matching condition and derived from the Schrödinger functional method ($N_f^c\sim 9)$ and the experimental analysis of the JLab group using Bjorken sum rule and GDH sum rule, and our lattice simulation($N_f^c\sim 3$) could be resolved by assuming the topological structure of the infrared fixed point is not that of $U(1)^3$ but that of $G_2$ with triality automorphism of octonions which appear in the product of quaternions. The agreement of the infrared fixed point of the running coupling measured in lattice simulations with use of the quaternion real condition and the prediction of the BLM renormalization theory might be due to the boundary condition on $S^3\times R$ manifold of quaternion. The form factor of a proton measured via Ward identity through the difference of the inverse propagator at momentum p+q/2 and at p-q/2 agrees with the phenomenological dipole fit.

hep-lat↗

Entropy of Chaotic Oscillations of Currents in the Chua Circuit and its HMM Analysis

We study entropy of chaotic oscillation of electrical currents in the Chua's circuit controlled by triggering a pulse that brings the orbit that goes onto an unstable branch back to a stable branch. A numerical simulation of the voltage of the two capacitors and the current that flows on an inductor of the Chua's circuit reveals various oscillation patterns as the conductance that is connected between the two capacitors and directly connected to an inductor is varied. At small conductance, the Lissajous graph of the voltage of the two capacitors shows a spiral, while at high conductance a double scroll pattern appears. The entropy of the current that flows on the inductor is alocal minimum in the spiral state which is in the steady state, while it is maximum in the stable double scroll state. The stable double scroll samples are analyzed by using the Hidden Markov Model (HMM) and the eigenvectors of the transition matrix of long time series are found to be strictly positive but those of unstable short time series have negative components. We thus confirm maximum entropy production in the double scroll of the longest time series around the right fixed point, while the local minimum entropy production occurs in the spiral around the left fixed point.

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Chiral Symmetry and BRST Symmetry Breaking, Quaternion Reality and the Lattice Simulation

We discuss that the deviation of the Kugo-Ojima color confinement parameter $u(0)$ from -1 in the case of quenched lattice simulation and the consistency with -1 in the case of full QCD simulation could be attributed to the boundary condition defined by fermions inside the region of $r<1$fm. By using the domain wall fermion propagator in lattice simulation, we show that the chiral symmetry breaking in the infrared can become manifest when one assumes that the left-handed fermion on the left wall and the right-handed fermion on the right wall are correlated by a self-dual gauge field. The relation between the infrared fixed point of the running coupling measured in lattice simulations, the prediction of the BLM renormalization theory, the conformal field theory with use of the t'Hooft anomaly matching condition in non-SUSY supersymmetric theory and the quaternion real condition are discussed.

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Self-dual gauge fields, domain wall fermion zero modes and the Kugo-Ojima confinement criterion

A new gauge fixing that imposes the U(1) real and quaternion real condition on the correlator of domain wall fermion on the left wall and right wall is proposed. The method is applied to the calculation of the mass function, the QCD effective coupling and the charge form factor of the proton. By assuming topological charge change $|Q|=1$, the charge form factor of the proton is approximately fitted by the dipole form factor. The difference of the Kugo-Ojima color confinement parameter in quenched simulation and in unquenched simulation is expected to be due to an anomaly caused by the vertex of two fermion zero modes and the Bose ghost/gluon.

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The self-dual gauge fields and the domain wall fermion zero modes

A new type of gauge fixing of the Coulomb gauge domain wall fermion system that reduces the fluctuation of the effective running coupling and the effective mass of arbitrary momentum direction including the region outside the cylinder cut region is proposed and tested in the $16^3\times 32\times 16$ gauge configurations of RBC/UKQCD collaboration. The running coupling at the lowest momentum point does not show infrared suppression and compatible with the experimental data extracted from the JLab collaboration. The source of the fluctuation of the effective mass near momentum $p=$0.6GeV region is expected to be due to the domain wall fermion zero modes.

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A study of quark-gluon vertices using the lattice Coulomb gauge domain wall fermion

I calculate the quark-gluon vertex of the tensor type $Γ(p,q)=g_3(p,q)p_4 \Slash{\Vec q}$, vector type $g_2(p,q)\Vec q$ and scalar type $g_1(p,q)$, for a small spacial momentum transfer $q=\bf q$ using the gauge configuration of the Domain Wall Fermion (DWF) provided by the RBC-UKQCD collaboration. The quark propagator of Coulomb gauge in the cylinder cut, i.e. the four momentum $p$ is directed along the diagonal of the hyper-cubic space has small fluctuation and I use this propagator in the evaluation of the operators by applying the non-perturbative renormalization method. The $q$ dependence of the running coupling $α_{s,g_1}(q)$ is compared with $α_I(q)$ measured by the ghost-gluon vertex in Coulomb gauge and $α_s(q)$ measured in Landau gauge.

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Propagator of the lattice domain wall fermion and the staggered fermion

The propagator of the domain wall fermion is calculated from the gauge configurations of the RBC-UKQCD collaborations with 2+1 dynamical flavors of $16^3\times 32\times 16$ lattice. The ambiguity of the phase is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The mass function becomes close to those of Kogut-Susskind fermion, but no anomalous behavior for $u/d$-quark mass and s-quark mass ratio close to 0.75 appears.

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Roles of the color antisymmetric ghost propagator in the infrared QCD

The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region is not purely color diagonal as in high energy region. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost-gluon-ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon propagator and the ghost propagator is investigated. Recent Dyson-Schwinger equation analysis suggests the ghost dressing function $G(0)=$ finite and no infrared enhancement or $α_G=0$. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as $< c\bar c>_r =-\frac{G(q^2)}{q^2}$ with $G(q^2)\propto q^{-2(1+α_G)}$ with $α_G = 0.5$, if the fixed point scenario is valid. I interpret the $α_G=0$ solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is $κ=α_G=-0.5$ and that of MILC is about -0.7. The implication for the Kugo-Ojima color confinement criterion, QCD effective coupling and the Slavnov identity are given.

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