Clifford algebras, spinors - Open Access .click

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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
wiley +1 more source

Quantum calculi and formalisms for system and network security: A bibliographic insights and synoptic review

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
wiley +1 more source

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
wiley +1 more source

Clifford Algebras and Their Applications to Lie Groups and Spinors [PDF]