scholarly journals VECTOR GENERATORS OF THE REAL CLIFFORD ALGEBRA Cℓ0,n

2014 ◽  
Vol 27 (4) ◽  
pp. 571-579
Author(s):  
Youngkwon Song ◽  
Doohann Lee
Keyword(s):  
Clifford Algebra ◽  
The Real ◽  
Real Clifford Algebra

scholarly journals Particle-antiparticle duality from an extra timelike dimension

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Marcos R. A. Arcodía ◽  
Mauricio Bellini
Keyword(s):  
Clifford Algebra ◽  
Extra Dimension ◽  
Complex Structure ◽  
Minkowski Spacetime ◽  
Gauge Condition ◽  
Extra Time ◽  
The Real ◽  
Dirac Particles ◽  
Real Clifford Algebra

Abstract It is a well known fact that the usual complex structure on the real Clifford Algebra (CA) of Minkowski spacetime can be obtained by adding an extra time-like dimension, instead of the usual complexification of the algebra. In this article we explore the consequences of this approach and reinterpret known results in this new context. We observe that Dirac particles and antiparticles at rest can be interpreted as eigenstates of the generator of rotations in the plane formed by the two time-like coordinates and find an effective finite scale for the extra dimension when no EM fields are present (without postulating compactness). In the case of non-vanishing EM fields, we find a gauge condition to preserve such a scale.

scholarly journals Real Clifford Algebra Cl[sub n,0], n = 2, 3(mod 4) Wavelet Transform

2009 ◽  
Author(s):  
Eckhard Hitzer ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Wavelet Transform ◽  
Clifford Algebra ◽  
Real Clifford Algebra

A note on Jordan algebras, three generations and exceptional periodicity

2020 ◽  
Vol 17 (05) ◽  
pp. 2050071
Author(s):  
Carlos Castro Perelman
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Clifford Algebra ◽  
Degrees Of Freedom ◽  
Jordan Algebras ◽  
The Real ◽  
Three Generations ◽  
Gauge Symmetries ◽  
The Standard Model ◽  
One To One

It is shown that the algebra [Formula: see text] based on the complexified Exceptional Jordan, and the complex Clifford algebra in 4D, is rich enough to describe all the spinorial degrees of freedom of three generations of fermions in 4D, and include additional fermionic dark matter candidates. Furthermore, the model described in this paper can account also for the Standard Model gauge symmetries. We extend these results to the Magic Star algebras of Exceptional Periodicity developed by Marrani–Rios–Truini and based on the Vinberg cubic [Formula: see text] algebras which are generalizations of exceptional Jordan algebras. It is found that there is a one-to-one correspondence among the real spinorial degrees of freedom of four generations of fermions in 4D with the off-diagonal entries of the spinorial elements of the [Formula: see text] [Formula: see text] of Vinberg matrices at level [Formula: see text]. These results can be generalized to higher levels [Formula: see text] leading to a higher number of generations beyond 4. Three [Formula: see text] of [Formula: see text] algebras and their conjugates [Formula: see text] were essential in the Magic Star construction of Exceptional Periodicity that extends the [Formula: see text] algebra to [Formula: see text] with [Formula: see text] integer.

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