Results 11 to 20 of about 2,501 (221)

Dirac algebra formalism for Two Higgs Doublet Models: The one-loop effective potential

Physics Letters B
We present a novel covariant bilinear formalism for the Two Higgs Doublet Model (2HDM) which utilises the Dirac algebra associated with the SL(2,C) group that acts on the scalar doublet field space.
Apostolos Pilaftsis
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Dirac Operators for the Dunkl Angular Momentum Algebra [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2022
We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements of the group algebra of the Pin cover of the Weyl group inherent to the rational Cherednik algebra. We prove an analogue of Vogan's conjecture for this family of operators and use this to show that the Dirac cohomology, when non-zero ...
Calvert, Kieran, De Martino, Marcelo
core   +8 more sources

Dirac Geometry I: Commutative Algebra

Peking Mathematical Journal, 2023
Abstract The purpose of this paper and its sequel is to develop the geometry built from the commutative algebras that naturally appear as the homology of differential graded algebras and, more generally, as the homotopy of algebras in spectra.
Lars Hesselholt, Piotr Pstra̧gowski
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Algebraic and analytic Dirac induction for graded affine Hecke algebras [PDF]

Journal of the Institute of Mathematics of Jussieu, 2013
AbstractWe define the algebraic Dirac induction map ${\mathrm{Ind} }_{D} $ for graded affine Hecke algebras. The map ${\mathrm{Ind} }_{D} $ is a Hecke algebra analog of the explicit realization of the Baum–Connes assembly map in the $K$-theory of the reduced ${C}^{\ast } $-algebra of a real reductive group using Dirac operators. The
Ciubotaru, D., Opdam, E.M., Trapa, P.E.
openaire   +7 more sources

Fermi-Bose duality of the Dirac equation and extended real Clifford-Dirac algebra [PDF]

Condensed Matter Physics, 2010
We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2 but also bosons of spin 1.
I.Yu. Krivsky, V.M. Simulik
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Dirac geometry II: coherent cohomology

Forum of Mathematics, Sigma
Dirac rings are commutative algebras in the symmetric monoidal category of $\mathbb {Z}$ -graded abelian groups with the Koszul sign in the symmetry isomorphism.
Lars Hesselholt, Piotr Pstrągowski
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Algebra de Clifford del espacio tiempo [PDF]

Momento, 1990
En un artículo previo, presentamos la estructura y relaciones básicas del algebra de Clifford Gn generada por el producto geométrico de los vectores de un espacio vectorial Vn sobre el cuerpo de los reales en la versión moderna de Hestenes. Este artículo
Ma. Carolina Spinel G.
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Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators

SciPost Physics Proceedings, 2023
In this paper we use the canonical complex structure $\mathbb{J}$ on $\mathbb{R}^{2n}$ to introduce a twist of the symplectic Dirac operator. This can be interpreted as the bosonic analogue of the Dirac operators on a Hermitian manifold.
Guner Muarem
doaj   +1 more source

Covariantization of quantized calculi over quantum groups [PDF]

Mathematica Bohemica, 2020
We introduce a method for construction of a covariant differential calculus over a Hopf algebra $A$ from a quantized calculus $da=[D,a]$, $a\in A$, where $D$ is a candidate for a Dirac operator for $A$.
Seyed Ebrahim Akrami, Shervin Farzi
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc   +2 more sources