- Homepage of Markus Maute -

Geometric Algebra

General:

• Some Clifford Algebra History - A. Diek, R. Kantowski

• Geometric Algebra Primer - J. Suter

• Geometric Algebra - T. F. Havel 1 2 3 4

• Geometric (Clifford) Algebra: A Practical Tool for Efficient Geometrical Representation - L. Dorst

• Geometric Algebra 1 - C. Doran

• A Survey of Geometric Algebra and Geometric Calculus - A. Macdonald

• Geometric Algebra with Conzilla - M. Nilsson

• Geometrische Algebra und die Rolle des Clifford-Produkts - F. Jung

• Clifford Algebras and Geometric Algebra - G. Aragon, J. L. Aragon, M. A. Rodriguez

• Geometric (Clifford) Algebra and its Applications - D. Lundholm

• How to Program Lorentz Transformations on a Computer - A. J. S. Hamilton

• The Geometric Associative Algebras od Euclidean Space - W. P. Joyce, P. H. Butler

• Basic Calculations on Clifford Algebra - G. Morales-Luna

 

People/Groups/Publications:

People:

Pertti Lounesto

E. M. S. Hitzer

William Pezzaglia

Matej Pavsic

Brannen Works

Groups:

• Cambridge University GA Research Group Publications

• Geometric Calculus in Japan Publications

Publications:

• B. Fauser

• J.B. Almeida

• W. A. Rodrigues

• R. D. Rocha

 

Geometry:

• Treatise of Plane geometry through Geometric Algebra

• Conformal Geometric Algebra and Applications

 

Analysis:

• Analytic Cliffordian Functions - G. Laville, E. Lehman

• Holomorphic Cliffordian Functions - G. Laiville, I. Ramadonov

• Geometric Algebra of one and Many Multivector Variables - J. Pesonen

 

Calculus:

• Geometric Algebra and Clifforms: with Application to the Gravitational Hamiltonian and Quasilocal Quantities - Tze-Ling Chong

• Geometric Algebra and Differential Forms: Translation and Gravitational Application - Yung-Kang Lin

• Variational Calculus in Geometric Algebra - R. Cabrera

• Multivector Differential Calculus - Hitzer

• Introductory Clifford Analysis - Ryan

• The Fundamental Theorem of Geometric Calculus via a Generalized Riemann Integral -Macdonald

 

Conformal GA:

• A Covariant Approach to Geometry using Geometric Algebra - A. Lasennby, J. Lasenby, R. Wareham

• Conformal Geometric Algebra and Applications- H. Li

 

Physics in general/ Spacetime Algebra:

• Spacetime Physics with Geometric Algebra - D. Hestenes

• Application of Clifford Algebras in Physics - W. E. Baylis

• Geometric Algebra and its Applications to Physics

• Geometric Algebra and its Applications to Mathematical Physics - C. Doran

• Choice of the best Geometry to Explain Physics - J. B. Almeida

• Imaginary Numbers are not Real. The Geometric Algebra of Spacetime - S. Gull, A. Lasenby, C. Doran

• Conformal Structures and Twistors in the Parameter Model of Spacetime - R. D. Rocha

• The Landscape of Theoretical Physics: A Global View; From Point Particles to the Brane World and Beyond, in Search of a Unifying Principle

• Physical Applications of a Generalized Clifford Calculus (Papapetrou equations and Metamorphic Curvature) - W. M. Pezzaglia

• Algebraic Structures and the Search for the Theory Of Everything: Clifford Algebras, Spinors and Supersymmetry - F. Toppan

• Can Physics Laws be Derived from Monogenic Functions- J. B. Almeida

• Lagrangian Formalism for Multiform Fields on Minkowski Spacetime - A. M. Moya, V. V. Fernandez, W. A. Rodrigues Jr.

• Dimensionally Democratic Calculus and Principles of Polydimensional Physics

• Clifford Algebras, Spinors and Fundamental Interactions : Twenty Years After

• Geometric Algebra and Covariant Methods in Physics and Cosmology

 

Gauge Theory & Standard Model:

• Clifford Algebra Implying Three Fermion Generations Revisited - W. Królikowski

• Space-Time Structure of Weak and Electromagnetic Interactions - Hestenes

• Gravity, Gauge Theories and Geometric Algebra - Lasenby, Doran, Gull

• Algebra of Matter - Schmeikal

• A gauge model with spinor group ... - N. G. Marchuk

 

QM/QFT:

• A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra

• Tensor-product vs. Geometric-product Coding

• A Treatise on Quantum Clifford Algebras - B. Fauser

• Clifford Geometric Parameterization of Inequivalent Vacua - B. Fauser

• The Mathematics of the Spinning Particle Problem - T. G. Erler IV

• On an Alternative Approach to the Relation between Bosons and Fermions: Employing Clifford Space - M. Pavsic

 

Dirac Equation:

• Dirac's Theory in Real Geometrical Formalism: Multivectors versus Spinors

• Multivector Solution to the Hyper Holomorphic Massive Dirac Equation

• The Construction of Spinors in Geometric Algebra - M. R. Francis, A. Kosowsky

• Spacetime Algebra and Electron Physics

• The Dirac Equation in Exterior Form

• Dirac Operators and Clifford Geometry - New Unifying Principles in Particle Physics

• Maxwell and Dirac Theories as an already Unified Theory

 

Gravity & Relativity:

• Geometric Algebra Techniques for General Relativity

• Applications of Geometric Algebra to Black Holes and Hawking Radiation

• How the Geometric Calculus Resolves the Ordering Ambiguity of Quantum Theory in Curved Space

• Applications of the Geometric Algebra to Rrelativistic Quantum Theory - S. S. Somaroo

• Standard Model and Gravity from Spinors - F. Nesti

• Projective Relativity: Present Status and Outlook - B. Fauser

• The Extended Relativity Theory in Clifford Spaces, The Extended Relativity Theory in Clifford Spaces: Reply to a Review by W. A. Rodrigues, Jr.

• Geometric Algebra: Spinors and the Positivity of Gravitational Energy - S.-N. Liang

• Higher Derivative Gravity and Torsion from the Geometry of C-spaces - C. Castro

 

Beyond the Spacetime Algebra

• Isotopic lifting of Clifford Algebras and Applications in Elementary Particle Mass Matrices - R. D. Rocha, J. Vaz Jr.

• A Geometric Basis for the Standard-Model Gauge Group - G. Trayling, W. E. Baylis

• Minimal Spin Gauge Theory - Clifford Algebra and Quantumchromodynamics - B. Schmeikal

 

GA & Informatics:

• Geometric Algebra and its Application to Computer Graphics - D. Hildenbrand, D. Fontijne, C. Perwas, L. Dorst

• Low-Level Image Processing with the Structure Multivector - M. Felsberg

 

Links:

Internal:

• Multiplication Tables

External:

• Hestenes files

• List of Geometric Algebra References

• Geometric Calculus International

• Welcome to CGAPS

• Alan Macdonald - Papers in Foundations of Physics and Geometric Algebra

 

Software:

• nklein software---products/geoma

• Geometric Algebra Calculator

• GABLE: A Matlab Tutorial for Geometric Algebra

• The Geompetric Algebra Java Package - E.MS Hitzer, G. Utama

 

Books:

• Clifford Algebras: Applications to Mathematics, Physics and Engineering

• Clifford Algebras and their Applications in Mathematical Physics

• Geometric Algebra (Clifford Algebra)

• Clifford Algebras with Numeric and Symbolic Computations - R. Ablamowicz, P. Lounesto, J. M. Parra

 

Not Classified (yet):

• Star Products and Geometric Algebra

• Geometric Algebra and Star Products on the Phase Space

• Hand-Eye Calibration

• dorst-mann-I.pdf (application/pdf-Objekt)

• Left-Ideals, Dirac Fermions and SU(2)-Flavour

• Quaternion Fourier Transform on Quaternion Fields and Generalizations

Dirac-Kähler Equation

Dirac Theory from a Field Theoretic Point of View

A Clifford Dyadic Superfield from Bilateral Interactions of Geometric Multispin Dirac Theory

• Geometry of Spinor Regularization - D. Hestenes, P. Lounesto

• Geometric-algebra

• Several Dirac Operators in Parablolic Geomtry

• Representations of Clifford Algebras and its Applications - S. Okubo

• The CPT Group in the de Sitter Space

• Degenerate Space-Time Paths and the Non-Locality of Quantum Mechanics in a Clifford Substructure of Space-Time - K. Borchsenius

• Tensor-Product vs. Geometric-Product Coding

 

Related topics: Quaternions, Octonions, Sedenions, Hypercomplex Numbers