Results 1 to 10 of about 245 (169)

New spinor classes on the Graf-Clifford algebra

Journal of High Energy Physics, 2018
Pinor and spinor fields are sections of the subbundles whose fibers are the representation spaces of the Clifford algebra of the forms, equipped with the Graf product.
R. Lopes, R. da Rocha
doaj   +1 more source

Developing GA-FuL: A Generic Wide-Purpose Library for Computing with Geometric Algebra

Mathematics
The Geometric Algebra Fulcrum Library (GA-FuL) version 1.0 is introduced in this paper as a comprehensive computational library for geometric algebra (GA) and Clifford algebra (CA), in addition to other classical algebras.
Ahmad Hosny Eid, Francisco G. Montoya
doaj   +1 more source

Geometric Algebra in Signal and Image Processing: A Survey

IEEE Access, 2019
Recently, Geometric Algebra (GA) has attracted more and more attention in the field of signal and image processing. GA can treat multi-dimensional signals in a holistic way to keep the correlations among multiple dimensions and avoid information loss. So
Rui Wang, Kaili Wang, Wenming Cao, Xiangyang Wang   +3 more
doaj   +1 more source

Solid Mechanics Segregated Solver Acceleration With Jacobian‐Free Newton‐Krylov

International Journal for Numerical Methods in Engineering, Volume 127, Issue 11, 15 June 2026.
ABSTRACT The segregated algorithm is a common approach for finite volumes solvers in solid mechanics, providing a memory‐efficient and straightforward implementation. Due to the inter‐coupling of the components through the source terms, it suffers from a slow convergence behavior in specific scenarios, such as geometries with significantly uneven ...
Andry Monlon, Alessandro Scolaro, Philip Cardiff, Ivor Clifford, Oskari Pakari, Mathieu Hursin   +5 more
wiley   +1 more source

Geometry of Supergravity and the Batalin–Vilkovisky Formulation of the N=1$\mathcal N=1$ Theory in Ten Dimensions

Fortschritte der Physik, Volume 74, Issue 5, May 2026.
ABSTRACT We provide full details of a BV formulation of N=1$\mathcal N=1$ supergravity in 10 dimensions, to all orders in fermions, built from the generalised geometry description of the theory. In contrast to standard treatments, we introduce neither the degrees of freedom corresponding to orthonormal frames for the metric nor the local Lorentz ...
Julian Kupka, Charles Strickland‐Constable, Fridrich Valach   +2 more
wiley   +1 more source

Deforming the Double‐Scaled SYK and Reaching the Stretched Horizon From Finite Cutoff Holography

Fortschritte der Physik, Volume 74, Issue 5, May 2026.
ABSTRACT We study the properties of the double‐scaled SYK (DSSYK) model under chord Hamiltonian deformations based on finite cutoff holography for general dilaton gravity theories with Dirichlet boundaries. The formalism immediately incorporates a lower‐dimensional analog of TT¯(+Λ2)$\text{T}\overline{\text{T}}(+\Lambda _2)$ deformations, denoted T2 ...
Sergio E. Aguilar‐Gutierrez
wiley   +1 more source

A New Geometric Algebra-Based Classification of Hand Bradykinesia in Parkinson’s Disease Measured Using a Sensory Glove

Algorithms
Parkinson’s disease (PD) is a chronic neurodegenerative disorder that progressively impairs motor functions. Clinical assessments have traditionally relied on rating scales such as the Movement Disorder Society Unified Parkinson Disease Rating Scale (MDS-
Giovanni Saggio, Paolo Roselli, Luca Pietrosanti, Alessandro Romano, Nicola Arangino, Martina Patera, Antonio Suppa   +6 more
doaj   +1 more source

Tessellation Groups, Harmonic Analysis on Non‐Compact Symmetric Spaces and the Heat Kernel in View of Cartan Convolutional Neural networks

Fortschritte der Physik, Volume 74, Issue 4, April 2026.
ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré, Federico Milanesio, Marcelo Oyarzo, Matteo Santoro, Mario Trigiante   +4 more
wiley   +1 more source

Noncommutative polygonal cluster algebras

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg, Dani Kaufman, Merik Niemeyer, Anna Wienhard   +3 more
wiley   +1 more source

Quantum GraviElectro Dynamics

Annalen der Physik, Volume 538, Issue 1, January 2026.
The BRST invariant Lagrangian of the gravitationally interacting U(1)$U(1)$ gauge theory, namely the Quantum GraviElectro Dynamics (QGED). The Yan–Mills theory with the Hilbert–Einstein gravitational Lagrangian, namely the Yang–Mills–Utiyama (YMU) theory, is defined and quantised using the standard procedure. The theory is perturbatively renormalisable,
Yoshimasa Kurihara
wiley   +1 more source