A Clifford algebra approach to general relativity

1989 ◽  
Vol 21 (1) ◽  
pp. 21-44 ◽  
Author(s):  
F. J. Chinea
Keyword(s):  
General Relativity ◽  
Clifford Algebra ◽  
Algebra Approach

scholarly journals Clifford algebra approach of 3D Ising model

2018 ◽  
Vol 29 (1) ◽  
Author(s):  
Zhidong Zhang ◽  
Osamu Suzuki ◽  
Norman H. March
Keyword(s):  
Ising Model ◽  
Clifford Algebra ◽  
Algebra Approach ◽  
3D Ising Model

scholarly journals Matrix 3-Lie superalgebras and BRST supersymmetry

2017 ◽  
Vol 14 (11) ◽  
pp. 1750160 ◽  
Author(s):  
Viktor Abramov
Keyword(s):  
Clifford Algebra ◽  
Lie Algebra ◽  
Vector Fields ◽  
Jacobi Identity ◽  
Lie Superalgebras ◽  
Infinite Dimensional ◽  
Algebra Approach ◽  
The Matrix ◽  
Infinite Dimensional Lie Algebra

Given a matrix Lie algebra one can construct the 3-Lie algebra by means of the trace of a matrix. In the present paper, we show that this approach can be extended to the infinite-dimensional Lie algebra of vector fields on a manifold if instead of the trace of a matrix we consider a differential 1-form which satisfies certain conditions. Then we show that the same approach can be extended to matrix Lie superalgebras [Formula: see text] if instead of the trace of a matrix we make use of the supertrace of a matrix. It is proved that a graded triple commutator of matrices constructed with the help of the graded commutator and the supertrace satisfies a graded ternary Filippov–Jacobi identity. In two particular cases of [Formula: see text] and [Formula: see text], we show that the Pauli and Dirac matrices generate the matrix 3-Lie superalgebras, and we find the non-trivial graded triple commutators of these algebras. We propose a Clifford algebra approach to 3-Lie superalgebras induced by Lie superalgebras. We also discuss an application of matrix 3-Lie superalgebras in BRST-formalism.

scholarly journals A Clifford algebra approach toN-dimensional crystallography

1993 ◽  
Vol 49 (s1) ◽  
pp. c341-c341
Author(s):  
A. Gómez ◽  
J. L. Aragón ◽  
F. Dávila ◽  
H. Terrones
Keyword(s):  
Clifford Algebra ◽  
Algebra Approach

scholarly journals Möbius gyrogroups: A Clifford algebra approach

2011 ◽  
Vol 328 (1) ◽  
pp. 230-253 ◽  
Author(s):  
M. Ferreira ◽  
G. Ren
Keyword(s):  
Clifford Algebra ◽  
Algebra Approach

Clifford algebra approach to twistors

1982 ◽  
Vol 23 (2) ◽  
pp. 231-242 ◽  
Author(s):  
R. Abl/amowicz ◽  
Z. Oziewicz ◽  
J. Rzewuski
Keyword(s):  
Clifford Algebra ◽  
Algebra Approach

Complex Boosts: A Hermitian Clifford Algebra Approach

2012 ◽  
Vol 23 (2) ◽  
pp. 339-362 ◽  
Author(s):  
Milton Ferreira ◽  
Frank Sommen
Keyword(s):  
Clifford Algebra ◽  
Algebra Approach

scholarly journals A Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies

2017 ◽  
Vol 32 (26) ◽  
pp. 1750159 ◽  
Author(s):  
Wei Lu
Keyword(s):  
Higgs Boson ◽  
Symmetry Breaking ◽  
Clifford Algebra ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Higgs Bosons ◽  
Fermion Mass ◽  
Tau Neutrino ◽  
Composite Higgs ◽  
Algebra Approach

We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford algebra, while ternary Clifford algebra-related flavor projection operators control allowable flavor-mixing interactions. There are three composite electroweak Higgs bosons resulted from top quark, tau neutrino, and tau lepton condensations. Each of the three condensations gives rise to masses of four different fermions. The fermion mass hierarchies within these three groups are determined by four-fermion condensations, which break two global chiral symmetries. The four-fermion condensations induce axion-like pseudo-Nambu–Goldstone bosons and can be dark matter candidates. In addition to the 125 GeV Higgs boson observed at the Large Hadron Collider, we anticipate detection of tau neutrino composite Higgs boson via the charm quark decay channel.

Sign in / Sign up

Export Citation Format

Share Document