zbMath0541.53059MaRDI QIDQ794307
Garret Sobczyk, David Hestenes
Publication date: 1984
Published in: Fundamental Theories of Physics (Search for Journal in Brave)
Spin(8) gauge field theory ⋮
Curvature calculations with spacetime algebra ⋮
A Clifford bundle approach to the wave equation of a spin \(1/2\) fermion in the de Sitter manifold ⋮
The construction of 3D conformal motions ⋮
On conformal curves in 2-dimensional de Sitter space ⋮
Generalization of the Dirac equation admitting isospin and color symmetries ⋮
Geometric algebra techniques in flux compactifications. II ⋮
Clifford algebras, multipartite systems and gauge theory gravity ⋮
Hermitian Clifford analysis on superspace ⋮
An extended implementation framework for geometric algebra operations on systems of coordinate frames of arbitrary signature ⋮
Discretization of Maxwell's equations for non-inertial observers using space-time algebra ⋮
Four forms make a universe ⋮
The cosmological constant from the extended theory of gravitation in Clifford spaces ⋮
Operator exponentials for the Clifford Fourier transform on multivector fields in detail ⋮
A conformal geometric algebra based clustering method and its applications ⋮
Metrics are Clifford algebra involutions ⋮
Algebraic programming of geometrical calculus and Clifford algebra ⋮
Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups ⋮
Clifford algebra, Lorentz transformation and unified field theory ⋮
Classical field theories from Hamiltonian constraint: local symmetries and static gauge fields ⋮
An improved formalism for quantum computation based on geometric algebra -- case study: Grover's search algorithm ⋮
Geometric algebra for multidimension-unified geographical information system ⋮
Hyperbolic geometry with geometric algebra ⋮
Four-dimensional geometric quantities versus the usual three-dimensional quantities: the resolution of Jackson's paradox ⋮
The inverse of a multivector: beyond the threshold \(p+q=5\) ⋮
Geometric algebra and star products on the phase space ⋮
Kinematic mappings for Cayley-Klein geometries via Clifford algebras ⋮
A product for special classes of monogenic functions and tensors ⋮
Spinor representations of Clifford algebras: A symbolic approach ⋮
Handling uncertain data in subspace detection ⋮
Deformations of the algebra of abstract vector variables ⋮
Clifford algebras and geometric algebra ⋮
Massive, non-ghost solutions for the Dirac field coupled self-consistently to gravity ⋮
Geometry of the hyperbolic spinors corresponding to alternative frame ⋮
Physical portrayal of computational complexity ⋮
Whitney algebras and Grassmann's regressive products ⋮
The Clifford-Fourier transform \({\mathcal {F}_0}\) and monogenic extensions ⋮
Constructing Voronoi diagrams from hollow spheres using conformal geometric algebra ⋮
Motor estimation using heterogeneous sets of objects in conformal geometric algebra ⋮
A conformal geometric algebra code generator comparison for virtual character simulation in mixed reality ⋮
Double conformal geometric algebra ⋮
General steerable two-sided Clifford Fourier transform, convolution and mustard convolution ⋮
The integration of angular velocity ⋮
Generalizations of Schwarzschild and (anti) de Sitter metrics in Clifford spaces ⋮
On Einstein algebras and relativistic spacetimes ⋮
Quaternion typification of Clifford algebra elements ⋮
Spin description in the star product and path integral formalisms ⋮
Index and wrapping number for paravectorvalued symbols ⋮
Clifford analysis on super-space ⋮
Inverse scattering and Clifford analysis ⋮
Fundamental representations and algebraic properties of biquaternions or complexified quaternions ⋮
Generating fractals using geometric algebra ⋮
Annihilators for harmonic differential forms via Clifford analysis ⋮
Extensions of the general method of generating Clifford algebras and comparisons with various existing methods ⋮
Fixed-size quadruples for a new, hardware-oriented representation of the 4D Clifford algebra ⋮
Kaluza-Klein theory without extra dimensions: curved Clifford space ⋮
Relativistic quantum physics with hyperbolic numbers ⋮
Spinors in the hyperbolic algebra ⋮
Nonlinear Bogolyubov-Valatin transformations: two modes ⋮
Geometric preprocessing and neurocomputing for pattern recognition and pose estimation. ⋮
Modeling the 3D kinematics of the eye in the geometric algebra framework. ⋮
Complex Lorentz rotations on vectors\(\oplus\)pseudovectors ⋮
Generalized projection operators in geometric algebra ⋮
All in action ⋮
Consistently oriented dart-based 3D modelling by means of geometric algebra and combinatorial maps ⋮
Projective geometry with Clifford algebra ⋮
The design of linear algebra and geometry ⋮
Automated theorem proving practice with null geometric algebra ⋮
A Clifford bundle approach to the differential geometry of branes ⋮
Registration of 3D points using geometric algebra and tensor voting ⋮
Multivector and multivector matrix inverses in real Clifford algebras ⋮
Dirac-Hestenes spinor fields on Riemann-Cartan manifolds ⋮
The problem of defining abstract bivectors ⋮
Monogenic differential operators ⋮
Fundamental theorem of calculus ⋮
In memoriam Jaime Keller (1936-2011) ⋮
Unconventional approach to orbital-free density functional theory derived from a model of extended electrons ⋮
Algebraic structures on space-time algebra ⋮
Topics on hyperbolic function theory in geometric algebra with a positive signature ⋮
Star products and geometric algebra ⋮
Multivector differential calculus ⋮
Reality as complex space ⋮
The signal multi-vector ⋮
Unified spatial intersection algorithms based on conformal geometric algebra ⋮
Existence and uniqueness results for quaternion-valued nonlinear impulsive differential systems ⋮
A geometric product formulation for spatial pythagorean hodograph curves with applications to Hermite interpolation ⋮
A Clifford algebraic framework for Coxeter group theoretic computations. ⋮
Tutorial on geometric calculus ⋮
Spin geometry and image processing ⋮
Detection of outer rotations on 3D-vector fields with iterative geometric correlation and its efficiency ⋮
Vortex detection in vector fields using geometric algebra ⋮
Multivectorial representation of Lie groups ⋮
The fundamental theorem of geometric calculus via a generalized Riemann integral ⋮
Einstein's equations and Clifford algebra ⋮
The geometry of light paths for equiangular spirals ⋮
The geometric content of the electron theory. II: Theory of the electron from start ⋮
Geometric analogue of holographic reduced representation ⋮
Higher derivative gravity and torsion from the geometry of \(C\)-spaces ⋮
The difference between the standard and the Lorentz transformations of the electric and the magnetic fields ⋮
Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field \(F\) with an explanation of the Trouton-Noble experiment ⋮
On factorization of multivectors in Cl(3,0), Cl(1,2) and Cl(0,3), by exponentials and idempotents ⋮
Graded symmetry groups: plane and simple ⋮
A geometric algebra approach to invariance control in sliding regimes for switched systems ⋮
Abilov's estimates for the Clifford-Fourier transform in real Clifford algebras analysis ⋮
Dynamics analysis of delayed fuzzy Clifford-valued model: a case of Equi-Weyl almost periodic environment ⋮
On Spacetime algebra and its relations with negative masses ⋮
Matchgate shadows for fermionic quantum simulation ⋮
Beurling's theorem in the Clifford algebras ⋮
Dimensional scaffolding of electromagnetism using geometric algebra ⋮
Heron's formula in higher dimensions ⋮
The supergeometric algebra: the square root of the geometric algebra ⋮
On noncommutative Vieta theorem in geometric algebras ⋮
Complementary orientations in geometric algebras ⋮
An ordered tuple construction of geometric algebras ⋮
On factorization of multivectors in Cl(2,1)$$ Cl\left(2,1\right) $$, by exponentials and idempotents ⋮
Connections between matrix products for 3-vectors and geometric algebra ⋮
On the spectrum of DW Hamiltonian of quantum SU(2) gauge field ⋮
On some Lie groups in degenerate Clifford geometric algebras ⋮
A generalization of Euler's formula in Clifford algebras ⋮
Modulus of smoothness and approximation theorems in Clifford analysis ⋮
Platonic solids generate their four-dimensional analogues ⋮
From the Trinity ( A 3 , B 3 , H 3 ) to an ADE correspondence ⋮
Classical field theories from Hamiltonian constraint: Canonical equations of motion and local Hamilton–Jacobi theory ⋮
A geometric approach for the analysis and computation of the intrinsic camera parameters ⋮
Motor algebra approach for visually guided robotics ⋮
Reflections in conics, quadrics and hyperquadrics via Clifford algebra ⋮
An extension of Mobius--Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library ⋮
\(f\)-algebra structure on hyperbolic numbers ⋮
Clifford algebra is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups ⋮
Calculation of quantum eigens with geometrical algebra rotors ⋮
The genesis of geometric algebra: a personal retrospective ⋮
Coordinate free integrals in geometric calculus ⋮
Composing surfaces with conformal rotors ⋮
Matrices of \(\mathrm{SL}(4,\mathbb R)\) that are the product of two skew-symmetric matrices ⋮
Geometric calculus of the Gauss map ⋮
Clifford multivector toolbox (for MATLAB) ⋮
Embedded coprocessors for native execution of geometric algebra operations ⋮
Inverse kinematics for a 6-DOF walking humanoid robot leg ⋮
Parallel Clifford support vector machines using the Gaussian kernel ⋮
Automatic multivector differentiation and optimization ⋮
Application of geometric algebra to the electroweak sector of the standard model of particle physics ⋮
Hamiltonian constraint formulation of classical field theories ⋮
Geometric algebra techniques in flux compactifications ⋮
Lyapunov stability: a geometric algebra approach ⋮
Formalizing geometric algebra in Lean ⋮
A Concise Parametrization of Affine Transformation ⋮
Spinors and multivectors as a unified tool for spacetime geometry and for elementary particle physics ⋮
Свертки по рангам и кватернионным типам в алгебрах Клиффорда ⋮
On the coupling of relativistic particle to gravity and Wheeler–DeWitt quantization ⋮
A Clifford algebra approach to the classical problem of a charge in a magnetic monopole field ⋮
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The radial algebra as an abstract framework for orthogonal and Hermitian Clifford analysis ⋮
Nonlinear half-dirichlet problems for first order elliptic equations in the unit ball of Rm(m≥3) ⋮
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Real spinors and real Dirac equation ⋮
Exploring novel surface representations via an experimental ray-tracer in CGA ⋮
Structure of factor algebras and Clifford algebra ⋮
Unitary geometric algebra ⋮
PLANAR IMMERSIONS WITH PRESCRIBED CURL AND JACOBIAN DETERMINANT ARE UNIQUE ⋮
On superluminal particles and the extended relativity theories ⋮
Monte Carlo geometry modeling for particle transport using conformal geometric algebra ⋮
A broad class of discrete-time hypercomplex-valued Hopfield neural networks ⋮
The color monogenic signal: application to color edge detection and color optical flow ⋮
A geometric algebra model for the image formation process of paracatadioptric cameras ⋮
Development of the method of quaternion typification of Clifford algebra elements ⋮
A note on Laurent series of the octonionic analytic functions ⋮
Clifford valued shearlet transform ⋮
Geometric invariant decomposition of SU(3) ⋮
Calculation of elements of spin groups using method of averaging in Clifford's geometric algebra ⋮
Projection factors and generalized real and complex Pythagorean theorems ⋮
Spacetime geometry with geometric calculus ⋮
Real Clifford windowed Fourier transform ⋮
A general geometric Fourier transform convolution theorem ⋮
A generalised methodology using conformal geometric algebra for mathematical chemistry ⋮
A Clifford algebra-based mathematical model for the determination of critical temperatures in superconductors ⋮
Leveraging prior known vector Green functions in solving perturbed Dirac equation in Clifford algebra ⋮
On a class of quaternionic positive definite functions and their derivatives ⋮
On Erdos' ten-point problem ⋮
Multivariate modelling of the trace element chemistry of arsenopyrite from gold deposits using higher-dimensional algebras ⋮
Pauli theorem in the description of \(n\)-dimensional spinors in the Clifford algebra formalism ⋮
Expressing the operations of quantum computing in multiparticle geometric algebra. ⋮
Berezin integral as a limit of Riemann sum ⋮
Generalized Weierstrass representation for surfaces in terms of Dirac-Hestenes spinor field ⋮
Quadratic Lagrangians and topology in gauge theory gravity ⋮
Differential Forms and Clifford Analysis ⋮
Blade products and angles between subspaces ⋮
Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension ⋮
Operators and field equations in the electroweak sector of particle physics ⋮
Monogenic Differential Calculus ⋮
Non-contextual and local hidden-variable model for the Peres-Mermin and Greenberger-Horne-Zeilinger systems ⋮
Space-time geometry and some applications of Clifford algebra in physics ⋮
The construction of spinors in geometric algebra ⋮
Using raising and lowering operators from geometric algebra for electroweak theory in particle physics ⋮
The existence and global exponential stability of \(\mu \)-pseudo almost periodic solutions of Clifford-valued semi-linear delay differential equations and an application ⋮
Conformal geometric algebra for robotic vision ⋮
Motor algebra approach for computing the kinematics of robot manipulators ⋮
Three-dimensional quadrics in extended conformal geometric algebras of higher dimensions from control points, implicit equations and axis alignment ⋮
Maxwell's equations are universal for locally conserved quantities ⋮
Implementation and evaluation of medical imaging techniques based on conformal geometric algebra ⋮
Dynamics of 3D sliding beams undergoing large overall motions ⋮
On inner automorphisms preserving fixed subspaces of Clifford algebras ⋮
Differential Methods for Multi-dimensional Visual Data Analysis ⋮
The proof that Maxwell equations with the 3D \({\mathbf E}\) and \({\mathbf B}\) are not covariant upon the Lorentz transformations but upon the standard transformations: the new Lorentz invariant field equations ⋮
Total least squares fitting of \(k\)-spheres in \(n\)-D Euclidean space using an \((n+2)\)-D isometric representation ⋮
Clifford algebra valued boundary integral equations for three-dimensional elasticity ⋮
Energy-momentum complex in general relativity and gauge theory ⋮
A generalised quaternion and Clifford algebra based mathematical methodology to effect multi-stage reassembling transformations in parallel robots ⋮
Monogenic Curvature Tensor as Image Model ⋮
Basis-free solution to general linear quaternionic equation ⋮
A geometric algebra based higher dimensional approximation method for statics and kinematics of robotic manipulators ⋮
An explicit realization of spinor spaces and its application to clifford analysis ⋮
On Bishop frame of a pseudo null curve in Minkowski space-time ⋮
Determining conformal transformations in Rn from minimal correspondence data ⋮
Spinor approch to gravitational motion and precession ⋮
A Formalization of Grassmann-Cayley Algebra in COQ and Its Application to Theorem Proving in Projective Geometry ⋮
Geometric algebra techniques for general relativity ⋮
Affine spinor decomposition in three-dimensional affine geometry ⋮
A General Geometric Fourier Transform ⋮
Differential operators, their fundamental solutions and related integral representations in Clifford analysis ⋮
Pose estimation in conformal geometric algebra. I: The stratification of mathematical spaces ⋮
Dynamical symmetry breaking and negative cosmological constant ⋮
Pose estimation of 3D free-form contours ⋮
Besicovitch almost periodic stochastic processes and almost periodic solutions of Clifford-valued stochastic neural networks ⋮
On conjugate complex time. III: Superstrings and complex Lorentz transformation ⋮
New applications of Clifford's geometric algebra ⋮
M, the power definition in geometric algebra that unveils the shortcomings of the nonsinusoidal apparent power \(S\) ⋮
Multi-modal medical image fusion based on geometric algebra discrete cosine transform
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