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Distributions of Dirac operator eigenvalues [PDF]
Physics Letters B, 2004 The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions which are stated.
Akemann, G., Damgaard, P.H.
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Matrix model and Yukawa couplings on the noncommutative torus
Journal of High Energy Physics, 2019 The IKKT model is proposed as a non-perturbative formulation of superstring theory. We propose a Dirac operator on the noncommutative torus, which is consistent with the IKKT model, based on noncommutative geometry.
Masaki Honda
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Dirac signal processing of higher-order topological signals
New Journal of Physics, 2023 Higher-order networks can sustain topological signals which are variables associated not only to the nodes, but also to the links, to the triangles and in general to the higher dimensional simplices of simplicial complexes.
Lucille Calmon +2 more
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DIRAC OPERATOR IN MATRIX GEOMETRY [PDF]
International Journal of Geometric Methods in Modern Physics, 2005 We review the construction of the Dirac operator and its properties in Riemannian geometry, and show how the asymptotic expansion of the trace of the heat kernel determines the spectral invariants of the Dirac operator and its index. We also point out that the Einstein–Hilbert functional can be obtained as a linear combination of the first two ...
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Czechoslovak Journal of Physics, 2000 To appear in the Proceedings of the Quantum Groups And Integrable Systems meeting in Prag, June 22-24 2000.
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The microscopic dirac operator spectrum [PDF]
Nuclear Physics B - Proceedings Supplements, 2002 We review the exact results for microscopic Dirac operator spectra based on either Random Matrix Theory, or, equivalently, chiral Lagrangians. Implications for lattice calculations are discussed.
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Completeness Theorems for Impulsive Dirac Operator with Discontinuity
AxiomsIn this work, the discontinuous Dirac operator with weight is studied. We prove the completeness theorems of the system of eigenfunctions for the discontinuous Dirac operator.
Kai Wang +3 more
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Dirac Operator on Embedded Hypersurfaces [PDF]
Mathematical Research Letters, 2001 New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of Atiyah-Patodi-Singer type.
Hijazi, Oussama +2 more
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Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications
International Journal of Mathematics and Mathematical Sciences, 2007 Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers.
M. Aslam Chaudhry, Asghar Qadir
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Advanced Functional Materials, EarlyView.A spin group (SG)‐based mechanism is proposed to realize a single pair of Weyl points. PT‐symmetric nodal lines (NLs) persist under T‐breaking, protected by the combination of SG and P symmetry. When considering spin‐orbit coupling, the SG‐protected NL will split into Weyl points, which will also induce anomalous transport phenomena arising from ...
Shifeng Qian +6 more
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