Classic Groups: Clifford Algebras, Projective Quadrics, and Spin Groups

2007 ◽  
pp. 1-70
Author(s):  
Pierre Anglè
Keyword(s):  
Clifford Algebras ◽  
Spin Groups

Quantum spinors and spin groups from quantum Clifford algebras

1997 ◽  
Vol 30 (18) ◽  
pp. 6451-6474 ◽  
Author(s):  
A Criscuolo ◽  
M Durdevic ◽  
M Rosenbaum ◽  
J D Vergara
Keyword(s):  
Clifford Algebras ◽  
Spin Groups

scholarly journals Real Clifford Algebras and Their Spinors for Relativistic Fermions

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 168
Author(s):  
Stefan Floerchinger
Keyword(s):  
Clifford Algebra ◽  
Clifford Algebras ◽  
Spin Groups ◽  
Mathematical Structures ◽  
Matrix Algebras ◽  
Space And Time ◽  
The Relationship ◽  
Real Complex

Real Clifford algebras for arbitrary numbers of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real, complex or quaternionic type. Spinors are defined as elements of minimal or quasi-minimal left ideals within the Clifford algebra and as representations of the pin and spin groups. Two types of Dirac adjoint spinors are introduced carefully. The relationship between mathematical structures and applications to describe relativistic fermions is emphasized throughout.

scholarly journals On the Problem of Choosing Subgroups of Clifford Algebras for Applications in Fundamental Physics

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
Robert Arnott Wilson
Keyword(s):  
Quantum Mechanics ◽  
Symmetry Breaking ◽  
Physical Theory ◽  
Clifford Algebras ◽  
Complex Numbers ◽  
Spin Groups ◽  
Fundamental Physics ◽  
Dirac Algebra ◽  
Fundamental Properties ◽  
The Many

AbstractClifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. An algebraist’s perspective on the many subgroups and subalgebras of Clifford algebras may suggest ways in which they might be applied more widely to describe the fundamental properties of matter. I do not claim to build a physical theory on top of the fundamental algebra, and my suggestions for possible physical interpretations are indicative only, and may not work. Nevertheless, both the existence of three generations of fermions and the symmetry-breaking of the weak interaction seem to emerge naturally from an extension of the Dirac algebra from complex numbers to quaternions.

Sign in / Sign up

Export Citation Format

Share Document