A Lichnerowicz vanishing theorem for the maximal Roe algebra
Sign Up to like & getrecommendations! Published in 2022 at "Mathematische Annalen"
DOI: 10.1007/s00208-021-02333-0
Abstract: We show that if a countable discrete group acts properly and isometrically on a spin manifold of bounded Riemannian geometry and uniformly positive scalar curvature, then, under a suitable condition on the group action, the… read more here.
Keywords: roe algebra; lichnerowicz vanishing; dirac operator; roe ... See more keywords
Lower bounds for the eigenvalue estimates of the submanifold Dirac operator
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DOI: 10.1007/s00209-021-02752-4
Abstract: We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, we can… read more here.
Keywords: submanifold dirac; bounds eigenvalue; dirac operator; lower bounds ... See more keywords
Geometric Dirac operator on the fuzzy sphere
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DOI: 10.1007/s11005-021-01499-7
Abstract: We construct a Connes spectral triple or ‘Dirac operator’ on the non-reduced fuzzy sphere $$\mathbb {C}_\lambda [S^2]$$ C λ [ S 2 ] as realised using quantum Riemannian geometry with a central quantum metric g… read more here.
Keywords: dirac operator; fuzzy sphere; operator fuzzy; dirac ... See more keywords
Cauchy Kernel of Slice Dirac Operator in Octonions with Complex Spine
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DOI: 10.1007/s11785-019-00977-0
Abstract: Holomorphic theory of one complex variable has a canonical extension to quaternions via the book structure in which the quaternions can be expressed as the union of complex planes through the common real axis. It… read more here.
Keywords: dirac operator; cauchy; slice dirac; operator ... See more keywords
Inverse problems for Dirac operator with the potential known on an interior subinterval
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DOI: 10.1007/s13324-017-0188-2
Abstract: The inverse spectral problems for Dirac operator with the potential known on an interior subinterval are considered. We prove that the potential on the entire interval and boundary conditions are uniquely determined in terms of… read more here.
Keywords: problems dirac; potential known; operator potential; interior subinterval ... See more keywords
The Dirac operator on locally reducible Riemannian manifolds
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2019.01.004
Abstract: In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are… read more here.
Keywords: operator; riemannian manifolds; locally reducible; operator locally ... See more keywords
A Discrete Extrinsic and Intrinsic Dirac Operator
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DOI: 10.1080/10586458.2020.1727798
Abstract: In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavour (that comes with spin transformations to comformally transfrom immersions) and… read more here.
Keywords: intrinsic dirac; dirac operator; discrete extrinsic; operator ... See more keywords
Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background
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DOI: 10.1103/physrevd.100.094501
Abstract: We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a… read more here.
Keywords: lattice dirac; lattice; dirac; dirac operator ... See more keywords
Spectral Properties of the Dirac Operator on the Real Line
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DOI: 10.1134/s0012266121020026
Abstract: We study the asymptotics of the spectrum of the Dirac operator on the real line with a potential in $$L_2 $$ . It is shown that the spectrum of such an operator lies in a… read more here.
Keywords: operator real; spectral properties; real line; properties dirac ... See more keywords
On the Spectrum of Two-Point Boundary Value Problems for the Dirac Operator
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DOI: 10.1134/s0012266121080036
Abstract: We consider the spectral problem for a Dirac operator with arbitrary two-point boundary conditions and an arbitrary complex-valued integrable potential. The existence of nontrivial boundary value problems of this type with an unbounded growth of… read more here.
Keywords: dirac operator; boundary value; two point; point boundary ... See more keywords
Distribution law of the Dirac eigenmodes in QCD
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DOI: 10.1142/s0217751x18500549
Abstract: The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks–Casher relation. At the same time, the distribution of the near-zero modes is well described… read more here.
Keywords: dirac operator; sbcs; distribution; near zero ... See more keywords