Results 21 to 30 of about 115 (111)
, 2011 Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses.
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On the Jucys–Murphy method and fusion procedure for the Sergeev superalgebra
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract We use the Jucys–Murphy elements to construct a complete set of primitive idempotents for the Sergeev superalgebra Sn${\mathcal {S}}_n$. We produce seminormal forms for the simple modules over Sn${\mathcal {S}}_n$ and over the spin symmetric group algebra with explicit constructions of basis vectors.
Iryna Kashuba +2 more
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Clifford Algebras, Spinors and Fundamental Interactions: Twenty Years After [PDF]
Advances in Applied Clifford Algebras, 2009 This is a short review of the algebraic properties of Clifford algebras and spinors. Their use in the description of fundamental physics (elementary particles) is also summarized. Lecture given at the ICCA7 conference, Toulouse (23/05/2005)
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What can we Learn from Quantum Convolutional Neural Networks?
Advanced Quantum Technologies, Volume 8, Issue 7, July 2025.Quantum Convolutional Neural Networks have been long touted as one of the premium architectures for quantum machine learning (QML). But what exactly makes them so successful for tasks involving quantum data? This study unlocks some of these mysteries; particularly highlighting how quantum data embedding provides a basis for superior performance in ...
Chukwudubem Umeano +3 more
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Clifford Algebras, Spinors and $Cl(8,8)$ Unification
, 2021 It is shown how the vector space $V_{8,8}$ arises from the Clifford algebra $Cl(1,3)$ of spacetime. The latter algebra describes fundamental objects such as strings and branes in terms of their $r$-volume degrees of freedom, $x^{ _1 _2 ... _r}$ $\equiv x^M$, $r=0,1,2,3$, that generalizethe concept of center of mass.
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A characterization of some finite simple groups by their character codegrees
Mathematische Nachrichten, Volume 298, Issue 4, Page 1356-1369, April 2025.Abstract Let G$G$ be a finite group and let χ$\chi$ be a complex irreducible character of G$G$. The codegree of χ$\chi$ is defined by cod(χ)=|G:ker(χ)|/χ(1)$\textrm {cod}(\chi)=|G:\textrm {ker}(\chi)|/\chi (1)$, where ker(χ)$\textrm {ker}(\chi)$ is the kernel of χ$\chi$.
Hung P. Tong‐Viet
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Double Copy From Tensor Products of Metric BV■‐Algebras
Fortschritte der Physik, Volume 73, Issue 1-2, February 2025.Abstract Field theories with kinematic Lie algebras, such as field theories featuring color–kinematics duality, possess an underlying algebraic structure known as BV■‐algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV■‐algebra.
Leron Borsten +5 more
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Curvature and Weitzenböck formula for spectral triples
Mathematische Nachrichten, Volume 297, Issue 12, Page 4582-4604, December 2024.Abstract Using the Levi‐Civita connection on the noncommutative differential 1‐forms of a spectral triple (B,H,D)$(\mathcal {B},\mathcal {H},\mathcal {D})$, we define the full Riemann curvature tensor, the Ricci curvature tensor and scalar curvature. We give a definition of Dirac spectral triples and derive a general Weitzenböck formula for them.
Bram Mesland, Adam Rennie
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IET Quantum Communication, Volume 5, Issue 4, Page 486-515, December 2024.Quantum calculi and formalisms aid in designing and analysing new cryptographic protocols for blockchain, assessing the feasibility and security of quantum algorithms, and building a quantum‐safe blockchain system. Bibliometric analysis is performed using R language and automated tools to identify key institutions, authors, organisations, and ...
Adarsh Kumar +2 more
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Hypercomplex operator calculus for the fractional Helmholtz equation
Mathematical Methods in the Applied Sciences, Volume 47, Issue 14, Page 11439-11472, 30 September 2024.In this paper, we develop a hypercomplex operator calculus to treat fully analytically boundary value problems for the homogeneous and inhomogeneous fractional Helmholtz equation where fractional derivatives in the sense of Caputo and Riemann–Liouville are applied.
Nelson Vieira +3 more
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