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Relevant bibliographies by topics / Hodge-Dirac operator

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Academic literature on the topic 'Hodge-Dirac operator'

Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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Journal articles on the topic "Hodge-Dirac operator"

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Sushch, Volodymyr. "2D Discrete Hodge–Dirac Operator on the Torus." Symmetry 14, no. 8 (2022): 1556. http://dx.doi.org/10.3390/sym14081556.

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We discuss a discretization of the de Rham–Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge–Dirac and Laplace operators in which key geometric aspects of the continuum counterpart are captured. We provide and prove a discrete version of the Hodge decomposition theorem. The goal of this work is to develop a satisfactory discrete model of the de Rham–Hodge theory on manifolds that are homeomorphic to the torus. Special attention has been paid to discrete models on a combinatorial torus. In this particular case, w

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Cosmo, Fabio di, and Alessandro Zampini. "Dirac operators on the S3 and S2 spheres." International Journal of Geometric Methods in Modern Physics 14, no. 08 (2017): 1740005. http://dx.doi.org/10.1142/s0219887817400059.

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We describe both the Hodge–de Rham and the spin manifold Dirac operator on the spheres [Formula: see text] and [Formula: see text], following the formalism introduced by Kähler, and exhibit a complete spectral resolution for them in terms of suitably globally defined eigenspinors.

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Di Cosmo, Fabio, Giuseppe Marmo, Juan Manuel Pérez-Pardo, and Alessandro Zampini. "A Hodge–de Rham Dirac operator on the quantum SU(2)." International Journal of Geometric Methods in Modern Physics 15, no. 02 (2018): 1850030. http://dx.doi.org/10.1142/s0219887818500305.

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We describe how it is possible to define a Hodge–de Rham Dirac operator associated to a suitable Cartan-Killing metric form upon the exterior algebra over the quantum spheres [Formula: see text] equipped with a three-dimensional left covariant calculus.

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Leopardi, Paul, and Ari Stern. "The Abstract Hodge--Dirac Operator and Its Stable Discretization." SIAM Journal on Numerical Analysis 54, no. 6 (2016): 3258–79. http://dx.doi.org/10.1137/15m1047684.

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MALIK, R. P. "ONE-FORM ABELIAN GAUGE THEORY AS THE HODGE THEORY." International Journal of Modern Physics A 22, no. 21 (2007): 3521–62. http://dx.doi.org/10.1142/s0217751x07037135.

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We demonstrate that the two (1+1)-dimensional (2D) free 1-form Abelian gauge theory provides an interesting field theoretical model for the Hodge theory. The physical symmetries of the theory correspond to all the basic mathematical ingredients that are required in the definition of the de Rham cohomological operators of differential geometry. The conserved charges, corresponding to the above continuous symmetry transformations, constitute an algebra that is reminiscent of the algebra obeyed by the de Rham cohomological operators. The topological features of the above theory are discussed in t

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RODRIGUES, WALDYR A., and QUINTINO A. G. SOUZA. "AN AMBIGUOUS STATEMENT CALLED THE "TETRAD POSTULATE" AND THE CORRECT FIELD EQUATIONS SATISFIED BY THE TETRAD FIELDS." International Journal of Modern Physics D 14, no. 12 (2005): 2095–150. http://dx.doi.org/10.1142/s0218271805008157.

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The names tetrad, tetrads, cotetrads have been used with many different meanings in the physics literature, not all of them equivalent from the mathematical point of view. In this paper, we introduce unambiguous definitions for each of those terms, and show how the old miscellanea made many authors introduce in their formalism an ambiguous statement called the "tetrad postulate," which has been the source of much misunderstanding, as we show explicitly by examining examples found in the literature. Since formulating Einstein's field equations intrinsically in terms of cotetrad fields θa, a = 0

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Abreu-Blaya, Ricardo, Juan Bory-Reyes, and Michael Shapiro. "The Cauchy Transform for the Hodge/De Rham System and Some of its Properties." gmj 14, no. 1 (2007): 1–20. http://dx.doi.org/10.1515/gmj.2007.1.

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Abstract We study the analogue of the Cauchy transform for the theory of solutions of the Hodge/de Rham system in the case of a rectifiable surface of integration which additionally satisfies an Ahlfors/David regularity condition and we prove the Cauchy integral formula, the Plemelj/Privalov theorem and the Sokhotski/Plemelj theorem for it, as well as the necessary and sufficient condition for the possibility to extend a given 𝑘-form from such a surface to a harmonic 𝑘-form in the domain. A formula for the square of the singular Cauchy transform is given. The proofs of all these facts are base

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van Neerven, Jan, and Rik Versendaal. "$$L^p$$-Analysis of the Hodge–Dirac Operator Associated with Witten Laplacians on Complete Riemannian Manifolds." Journal of Geometric Analysis 28, no. 4 (2017): 3109–38. http://dx.doi.org/10.1007/s12220-017-9947-4.

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LUSANNA, LUCA. "CLASSICAL YANG-MILLS THEORY WITH FERMIONS II: DIRAC’S OBSERVABLES." International Journal of Modern Physics A 10, no. 26 (1995): 3675–757. http://dx.doi.org/10.1142/s0217751x95001753.

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For pure Yang-Mills theory on Minkowski space-time, formulated in functional spaces where the covariant divergence is an elliptic operator without zero modes, and for a trivial principal bundle over the fixed time Euclidean space with a compact, semisimple, connected and simply connected structure Lie group, a Green function for the covariant divergence has been found. It allows one to solve the first class constraints associated with Gauss’ laws and to identify a connection-dependent coordinatization of the trivial principal bundle. In a neighborhood of the global identity section, by using c

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Cerejeiras, P., and J. Cnops. "Hodge—dirac operators for hyperbolic spaces." Complex Variables, Theory and Application: An International Journal 41, no. 3 (2000): 267–78. http://dx.doi.org/10.1080/17476930008815254.

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Dissertations / Theses on the topic "Hodge-Dirac operator"

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Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.

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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwells equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission pro

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Bandara, Lashi. "Geometry and the Kato square root problem." Phd thesis, 2013. http://hdl.handle.net/1885/10690.

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The primary focus of this thesis is to consider Kato square root problems for various divergence-form operators on manifolds. This is the study of perturbations of second-order differential operators by bounded, complex, measurable coefficients. In general, such operators are not self-adjoint but uniformly elliptic. The Kato square root problem is then to understand when the square root of such an operator, which exists due to uniform ellipticity, is comparable to its unperturbed counterpart. A remarkably adaptable operator-theoretic framework due to Axelsson, Keith and McIntosh sits in the ba

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Axelsson, Andreas. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." Phd thesis, 2002. http://hdl.handle.net/1885/46056.

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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface, in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission pr

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Morris, Andrew Jordan. "Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds." Phd thesis, 2010. http://hdl.handle.net/1885/8864.

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The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood--Paley--Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the o

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Books on the topic "Hodge-Dirac operator"

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Arhancet, Cédric, and Christoph Kriegler. Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99011-4.

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Arhancet, Cédric, and Christoph Kriegler. Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers. Springer International Publishing AG, 2022.

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Book chapters on the topic "Hodge-Dirac operator"

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Arhancet, Cédric, and Christoph Kriegler. "Boundedness of H ∞ Functional Calculus of Hodge-Dirac Operators." In Lecture Notes in Mathematics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99011-4_4.

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