Results 91 to 100 of about 5,272 (123)

Clifford Algebras and Spinor Operators

1996
This paper begins with a historical survey on Clifford algebras and a model on how to start an undergraduate course on Clifford algebras. The Dirac equation and the bilinear covariants are discussed. The Fierz identities are sufficient to reconstruct a Dirac spinor from its bilinear covariants, up to a phase.
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Clifford Algebras and Spinor Groups

2002
In this chapter, we generalise the quaternions by studying the real Clifford algebras, and our account of these is heavily influenced by the classic paper of Atiyah, Bott & Shapiro [3]; Porteous [23, 24] also provides an accessible description, as does Curtis [7] but there are some errors and omissions in that account. Lawson & Michelsohn [19] provides
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Gauge transformations of spinors within a Clifford algebraic structure

Journal of Physics A: Mathematical and General, 1999
The paper consists of 6 sections and 2 appendices. Section 1 analyzes the notion of algebraic spinors as minimal left ideals of Clifford algebras. In section 2 gauge transformations are considered as two-sided equivalence transformations of a complete algebra, including the spinors.
Chisholm, J. S. R., Farwell, R. S.
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LUCY: A Clifford Algebra Approach to Spinor Calculus

1996
LUCY is a MAPLE program that exploits the general theory of Clifford algebras to effect calculations involving real or complex spinor algebra and spinor calculus on manifolds in any dimension. It is compatible with both release 2 and release 3 of MAPLE V and incorporates a number of valuable facilities such as multilinearity of the Clifford product and
Schray, Jörg, Tucker, Robin, Wang, Charles   +2 more
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Clifford algebras, spinors and finite geometries

2008
The pleasant incidence properties of the finite projective geometry PG(m,2) are invoked in order to handle nicely certain commutativity/anti-commutativity aspects of the real Clifford algebras Cl(O,d), d = |PG(m,2)|= 2m+1 - 1 , m = 2,3, ...
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Spinor-valued and Clifford algebra-valued harmonic polynomials

Journal of Geometry and Physics, 2001
In the paper under review the author gives some decompositions of the spinor-valued and Clifford algebra-valued harmonic polynomials on \( \mathbb{R} ^n \) and proves that each component of the decompositions is an irreducible representation space with respect to the Lie group \( \text{Spin} (n) \).
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Parallel Transport of Algebraic Spinors on Clifford Manifolds

2001
A Clifford manifold is defined by a position-dependent frame field eμ(x) and metric g μν (x), satisfying the anti-commutation rule e μ ,e ν = g μν I At each point x, orthonormal basis vector sets define the tangent space and the spin group. The Riemannian and spin connections are defined by imposing covariance under coordinate and spin group ...
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Clifford Algebras, Pure Spinors and the Physics of Fermions

2004
The equations defining pure spinors are interpreted as equations of motion formulated on the lightcone of momentum space P = ℝ1, 9. Most of the equations for fermion multiplets, usually adopted by particle physics, are then naturally obtained and their properties, such as internal symmetries, charges, and families, appear to be due to the correlation ...
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Clifford Algebras and the Construction of the Basic Spinor and Semi-Spinor Modules

2000
Tensor powers of the defining module of a complex orthogonal Lie algebra can be used to construct all of the basic modules except for the spinor and semispinor modules. Thus, for the constructive representation theory of these simple Lie algebras, one must supplement the methods of tensor algebra with those of spinor algebra. For the simple complex Lie
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Clifford algebras and spinors

2012
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