Application of Clifford algebra and quaternion representations to (3+1)D non-destructive testing

ORAL

Abstract

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.

We adopt the Riesz Wavelet transform for image recognition of non-destructive testing.

Comparison with the quaternion Fourier transfer of Hitzer and the tensor renormalization group approach to classical lattice models is also discussed.

* Nihon Sangyo Kagaku Kenkyujo grant in aid.

Publication: arXiv:2310.10680
On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$

Presenters

  • Sadataka Furui

    Teikyo University

Authors

  • Sadataka Furui

    Teikyo University

  • Serge Dos Santos

    INSA val de Loire