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

Furui, Sadataka; Santos, Serge Dos

doi:10.48550/arxiv.2010.09487

Cited by 2 publications

(3 citation statements)

References 51 publications

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“…In nature, the chiral symmetry and self-adjoint operations play important roles and the quternion H is a useful tool, which clarifys the role of an extra dimension and conformal transformations. Non-linearity and solitonic waves in various domains are also important [127].…”

Section: Discussionmentioning

confidence: 99%

A Closer Look at Gluons

Furui

2021

Preprint

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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 electroweak theory, left handed leptons l L and neutrino ν 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) × U (1) symmetry. Charge of leptons and quarks define hypercharge Y , and via Higgs mechanism SU (2) L × U (1) Y symmetry forms U (1) em symmetry.Presence of J P = 3/2 + baryons, or N * ++ ∼ uuu suggests a new degree of freedom "color" for quarks, which follows SU (3) symmetry group. Hence the gluon fields are expressed as A a µ where a = 1, 2, • • • , 8 specify the color SU (3) bases, and µ are 4dimensional space-time coordinates. The quantum electrodynamics was extended to quantum chromo dynamics (QCD). Since ∂ µ A a µ is not a free field, the gauge theory requires ghosts that compensates unphysical degrees of freedom of gluons. Gluons, ghosts, leptons and quarks are related by Becchi-Rouet-Stora -Tyuitin (BRST) transformation of electroweak and strong interaction of the U (1) × SU (2) × SU (3) symmetric Faddeev-Popov Lagrangian.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 H, whose multiplication on 2 × 2 matrices of Dirac spinors on S 3 induces transformations. Instantons or sphalerons whose presence is expected from conformal equivalence of S 3 × R to R 4 are reviewed. An extension of the dynamics embedded in complex projective space is also discussed.

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Section: Discussionmentioning

confidence: 99%

A Closer Look at Gluons

Furui

2021

Preprint

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“…The convolution of a Khokhlov-Zaboltskaya solitonic wave obtained by Lapidus and Rudenko [12], and its TR solitonic wave show presence of anomalous zero mode [16], and detailed analysis of TR-NEWS convolution data will present hints on the gravitational anomaly suggested in [9].…”

Section: Introductionmentioning

confidence: 91%

“…However, in the case of 𝐵 type loops, we include the scalar term and consider the energytime transformation. We regard phonons as shock waves produced on Fermi surfaces and calculate plaquette actions derived from the fixed point action in 4𝐷 [17] at (2 + 1)𝐷 lattice points with the asymptotic high momentum action subtracted [16,18,19]. Link actions of 𝐵 type loops for large momenta are asymptotically zero, but they depend on the clockwise rotating (f-link) or counterclockwise rotating (e-link).…”

Section: Fixed Point Actions Of One Loopmentioning

confidence: 99%

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

Furui¹,

Santos²

2022

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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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 × 256 2D lattice points, which are expressed by quaternions 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.

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

Cited by 2 publications

References 51 publications

A Closer Look at Gluons

A Closer Look at Gluons

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

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