Ebook: Clifford Algebras with Numeric and Symbolic Computations

Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.

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Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.

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Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.

Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Counterexamples in Clifford Algebras with Clical....Pages 3-30
Front Matter....Pages 31-31
The Use of Computer Algebra and Clifford Algebra in Teaching Mathematical Physics....Pages 33-55
General Clifford Algebra and Related Differential Geometry Calculations with Mathematica ....Pages 57-67
Pauli-Algebra Calculations in MAPLE V....Pages 69-82
The Generative Process of Space-Time and Strong Interaction Quantum Numbers of Orientation....Pages 83-100
On a New Basis for a Generalized Clifford Algebra and its Application to Quantum Mechanics....Pages 101-110
Vector Continued Fraction Algorithms....Pages 111-119
LUCY: A Clifford Algebra Approach to Spinor Calculus....Pages 121-143
Computer Algebra in Spinor Calculations....Pages 145-154
Vahlen Matrices for Non-Definite Metrics....Pages 155-164
Front Matter....Pages 165-165
On Clifford Algebras of a Bilinear Form with an Antisymmetric Part....Pages 167-188
A Unipodal Algebra Package for Mathematica....Pages 189-199
Octonion X-Product Orbits....Pages 201-212
A Commutative Hypercomplex Algebra with Associated Function Theory....Pages 213-227
On Generalized Clifford Algebras — Recent Applications....Pages 229-231
Oriented Projective Geometry with Clifford Algebra....Pages 233-250
The Applications of Clifford Algebras to Crystallography Using Mathematica ....Pages 251-266
Front Matter....Pages 267-267
Orthonormal Basis Sets in Clifford Algebras....Pages 269-284
Complex Conjugation — Relative to What?....Pages 285-294
Object-Oriented Implementations of Clifford Algebras in C++: A Prototype....Pages 295-315
Back Matter....Pages 317-322

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Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.

Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Counterexamples in Clifford Algebras with Clical....Pages 3-30
Front Matter....Pages 31-31
The Use of Computer Algebra and Clifford Algebra in Teaching Mathematical Physics....Pages 33-55
General Clifford Algebra and Related Differential Geometry Calculations with Mathematica ....Pages 57-67
Pauli-Algebra Calculations in MAPLE V....Pages 69-82
The Generative Process of Space-Time and Strong Interaction Quantum Numbers of Orientation....Pages 83-100
On a New Basis for a Generalized Clifford Algebra and its Application to Quantum Mechanics....Pages 101-110
Vector Continued Fraction Algorithms....Pages 111-119
LUCY: A Clifford Algebra Approach to Spinor Calculus....Pages 121-143
Computer Algebra in Spinor Calculations....Pages 145-154
Vahlen Matrices for Non-Definite Metrics....Pages 155-164
Front Matter....Pages 165-165
On Clifford Algebras of a Bilinear Form with an Antisymmetric Part....Pages 167-188
A Unipodal Algebra Package for Mathematica....Pages 189-199
Octonion X-Product Orbits....Pages 201-212
A Commutative Hypercomplex Algebra with Associated Function Theory....Pages 213-227
On Generalized Clifford Algebras — Recent Applications....Pages 229-231
Oriented Projective Geometry with Clifford Algebra....Pages 233-250
The Applications of Clifford Algebras to Crystallography Using Mathematica ....Pages 251-266
Front Matter....Pages 267-267
Orthonormal Basis Sets in Clifford Algebras....Pages 269-284
Complex Conjugation — Relative to What?....Pages 285-294
Object-Oriented Implementations of Clifford Algebras in C++: A Prototype....Pages 295-315
Back Matter....Pages 317-322
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