On Jordan–Clifford Algebras, Three Fermion Generations with Higgs Fields and a $${{\mathrm {SU}(3) \times \mathrm {SU}(2)_L \times \mathrm {SU}(2)_R \times \mathrm {U}(1)}}$$ Model

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Carlos Castro Perelman
Keyword(s):  
Clifford Algebras ◽  
Higgs Fields

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

Isomorphisms of graded skew Clifford algebras

2020 ◽  
Vol 13 (5) ◽  
pp. 871-878
Author(s):  
Richard G. Chandler ◽  
Nicholas Engel
Keyword(s):  
Clifford Algebras

scholarly journals Iterants, Majorana Fermions and the Majorana-Dirac Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1373
Author(s):  
Louis H. Kauffman
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Clifford Algebras ◽  
Discrete Systems ◽  
Complex Numbers ◽  
Majorana Fermions ◽  
Matrix Algebras ◽  
Dirac Equations ◽  
Points Of View

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.

The classical problem of the charge and pole motion. A satisfactory formalism by Clifford algebras

1989 ◽  
Vol 220 (1-2) ◽  
pp. 195-199 ◽  
Author(s):  
W.A. Rodrigues ◽  
E. Recami ◽  
A. Maia ◽  
M.A.F. Rosa
Keyword(s):  
Clifford Algebras ◽  
Classical Problem ◽  
Pole Motion

Extension of Standard Model in multi-spinor field formalism — Visible and dark sectors

2016 ◽  
Vol 31 (18) ◽  
pp. 1630027
Author(s):  
Ikuo S. Sogami
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Dark Sector ◽  
Quadratic Interaction ◽  
Inflationary Phase ◽  
The Standard Model ◽  
Visible Sector ◽  
Field Formalism ◽  
Main Component ◽  
Higgs Fields

With multi-spinor fields which behave as triple-tensor products of the Dirac spinors, the Standard Model is extended so as to embrace three families of ordinary quarks and leptons in the visible sector and an additional family of exotic quarks and leptons in the dark sector of our Universe. Apart from the gauge and Higgs fields of the Standard Model symmetry G, new gauge and Higgs fields of a symmetry isomorphic to G are postulated to exist in the dark sector. It is the bi-quadratic interaction between visible and dark Higgs fields that opens a main portal to the dark sector. Breakdowns of the visible and dark electroweak symmetries result in the Higgs boson with mass 125 GeV and a new boson which can be related to the diphoton excess around 750 GeV. Subsequent to a common inflationary phase and a reheating period, the visible and dark sectors follow weakly-interacting paths of thermal histories. We propose scenarios for dark matter in which no dark nuclear reaction takes place. A candidate for the main component of the dark matter is a stable dark hadron with spin 3/2, and the upper limit of its mass is estimated to be 15.1 GeV/c2.

A Note on Generalized Clifford Algebras and Representations

1989 ◽  
Vol 17 (1) ◽  
pp. 93-102 ◽  
Author(s):  
S. Caenepeel ◽  
F. Van Oystaeyen
Keyword(s):  
Clifford Algebras

scholarly journals REPRESENTATIONS OF ALTERNATIVE CLIFFORD ALGEBRAS OF QUADRATIC FORMS

2014 ◽  
Vol 57 (3) ◽  
pp. 579-590 ◽  
Author(s):  
STACY MARIE MUSGRAVE
Keyword(s):  
Quadratic Form ◽  
Clifford Algebra ◽  
Algebraic Structure ◽  
Quadratic Forms ◽  
Clifford Algebras ◽  
Future Research ◽  
Octonion Algebras

AbstractThis work defines a new algebraic structure, to be called an alternative Clifford algebra associated to a given quadratic form. I explored its representations, particularly concentrating on connections to the well-understood octonion algebras. I finished by suggesting directions for future research.

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