Results 111 to 120 of about 249 (143)

Clifford algebraic spinor and the Dirac wave equations

Advances in Applied Clifford Algebras, 2001
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Yu, Xuegang, Zhang, Shuna, Huang, Qiunan
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Spinor representations of Clifford algebras: a symbolic approach

Computer Physics Communications, 1998
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Finite-dimensional Clifford Algebras and Spinors

2001
From the noncommutative geometric standpoint of Part III, commutative geometry and Clifford geometry are one and the same thing. So here we deal with their linear-algebraic and Lie-theoretic underpinnings, namely Clifford algebra. We chose not to dispense with it in this book, despite the existence of many excellent treatments, mainly for ease of ...
José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa   +2 more
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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 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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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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The Primitive Idempotents of the Clifford Algebras and the Amorphic Spinor Fiber Bundles

Reports on Mathematical Physics, 1988
We intend to clarify the ‘primitive idempotent’ method of defining spinor bundles as fields of minimal ideals in some Clifford algebra. In this, the fundamental notion of ‘geometric Clifford spinoriality group’, similar but not at all equivalent to that of ‘groupe de spinorialite’ defined by the author in [1, d], will appear.
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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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On the classification of Clifford algebras and their relation to spinors in n dimensions

Journal of Mathematical Physics, 1982
A classification of all the Clifford algebras is given in terms of Kronecker products of the quaternion and dihedral groups. The relationship to spinors in n dimensions is explicitly determined. We show that the real Clifford algebra in Minkowski spacetime is distinct from both the algebra of Dirac matrices and the algebra of Majorana matrices, and ...
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