24 Citations
Geometric (Clifford) algebra and its applications
- Mathematics
- 2006
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations…
Geometric (Cliord) algebra and its applications
- Mathematics
- 2006
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations…
Twistors in Geometric Algebra
- Mathematics
- 2008
Abstract.Twistors are re-interpreted in terms of geometric algebra as 4-d spinors with a position dependence. This allows us to construct their properties as observables of a quantum system. The…
A ] 1 0 M ay 2 00 6 Geometric ( Clifford ) algebra and its applications
- Mathematics
- 2006
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations…
1 3 A ug 2 01 9 Real spinors and real Dirac equation
- Mathematics
- 2019
In this article we draw attention to spinors, both in space and in spacetime, and advocate the approach of [5], in which they are regarded as elements of the even subalgebra of the real Clifford…
Two-State Quantum Systems Revisited: a Geometric Algebra Approach
- Mathematics, Physics
- 2020
We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as…
The five-dimensional Dirac equation in the theory of algebraic spinors
- Mathematics
- 2017
The Dirac equation is considered in five-dimensional spaces with signatures (2,3), (4,1) and (0,5). The algebraic spinor formalism with the application of fermionic variables is used as the basis of…
On Computable Geometric Expressions in Quantum Theory
- Mathematics
- 2019
Geometric Algebra and Calculus are mathematical languages that encode fundamental geometric relations that theories of physics must respect, and eliminate from our vocabulary those they do not. We…
Two-State Quantum Systems Revisited: A Clifford Algebra Approach
- Mathematics, Physics
- 2021
We revisit the topic of two-state quantum systems using the Clifford Algebra in three dimensions $$Cl_3$$
. In this description, both the quantum states and Hermitian operators are written as…
References
SHOWING 1-10 OF 27 REFERENCES
Scalar products of spinors and an extension of Brauer-Wall groups
- Mathematics
- 1981
The automorphism groups of scalar products of spinors are determined. Spinors are considered as elements of minimal left ideals of Clifford algebras on quadratic modules, e.g., on orthogonal spaces.…
Cli ord Algebras and the Classical Groups
- Mathematics
- 1995
The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper…
An Introduction to Spinors and Geometry with Applications in Physics
- Physics
- 1988
There is now a greater range of mathematics used in theoretical physics than ever. The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of…
States and operators in the spacetime algebra
- Physics
- 1993
The spacetime algebra (STA) is the natural, representation-free language for Dirac's theory of the electron. Conventional Pauli, Dirac, Weyl, and Majorana spinors are replaced by spacetime…
Geometric Algebra for Physicists
- Mathematics, Physics
- 2003
Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with…
Clifford Algebras and Spinors
- Mathematics
- 1997
A historical review of spinors is given together with a construction of spinor spaces as minimal left ideals of Clifford algebras. Spinor spaces of euclidean spaces over reals have a natural linear…
On the algebra of Dirac bispinor densities: Factorization and inversion theorems
- Mathematics
- 1985
The algebraic system formed by Dirac bispinor densities ρi≡ψΓiψ is discussed. The inverse problem—given a set of 16 real functions ρi, which satisfy the bispinor algebra, find the spinor ψ to which…
Orthogonal and Symplectic Clifford Algebras: Spinor Structures
- Mathematics
- 1990
Orthogonal and Symplectic Geometries.- Tensor Algebras, Exterior Algebras and Symmetric Algebras.- Orthogonal Clifford Algebras.- The Clifford Groups, the Twisted Clifford Groups and Their…
Lie-groups as Spin groups.
- Mathematics
- 1993
It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie group can be represented as a spin group. Thus, the computational power of geometric algebra is available…
REAL SPINOR FIELDS.
- Physics
- 1967
The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (−1)½ which appears explicitly in the Dirac equation. In the modification…