有边界流形的霍奇-狄拉克算子和达布罗夫斯基-西塔尔兹-扎莱基类型定理

IF 2.1 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

International Journal of Geometric Methods in Modern Physics Pub Date : 2024-03-13 DOI:10.1142/s0219887824501627

Tong Wu, Yong Wang

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引用次数: 0

摘要

Dabrowski 等人[霍奇-狄拉克算子的谱度量和爱因斯坦函数，预印本（2023 年），arXiv:2307.14877]给出了定向偶维黎曼流形上霍奇-狄拉克算子 d+δ 的微分形式的谱爱因斯坦双线性函数。在本文中，我们将 Dabrowski 等人的结果推广到有边界的 4 维定向黎曼流形的情况。此外，我们还给出了与有边界流形的霍奇-狄拉克算子相关的 Dabrowski-Sitarz-Zalecki- 型定理的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Hodge–Dirac operator and Dabrowski–Sitarz–Zalecki-type theorems for manifolds with boundary

Dabrowski et al. [Spectral metric and Einstein functionals for Hodge–Dirac operator, preprint (2023), arXiv:2307.14877] gave spectral Einstein bilinear functionals of differential forms for the Hodge–Dirac operator $d + δ$ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski et al. to the cases of 4-dimensional oriented Riemannian manifolds with boundary. Furthermore, we give the proof of Dabrowski–Sitarz–Zalecki-type theorems associated with the Hodge–Dirac operator for manifolds with boundary.

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来源期刊

International Journal of Geometric Methods in Modern Physics 物理-物理：数学物理

CiteScore

3.40

自引率

22.20%

发文量

274

审稿时长

6 months

期刊介绍： This journal publishes short communications, research and review articles devoted to all applications of geometric methods (including commutative and non-commutative Differential Geometry, Riemannian Geometry, Finsler Geometry, Complex Geometry, Lie Groups and Lie Algebras, Bundle Theory, Homology an Cohomology, Algebraic Geometry, Global Analysis, Category Theory, Operator Algebra and Topology) in all fields of Mathematical and Theoretical Physics, including in particular: Classical Mechanics (Lagrangian, Hamiltonian, Poisson formulations); Quantum Mechanics (also semi-classical approximations); Hamiltonian Systems of ODE''s and PDE''s and Integrability; Variational Structures of Physics and Conservation Laws; Thermodynamics of Systems and Continua (also Quantum Thermodynamics and Statistical Physics); General Relativity and other Geometric Theories of Gravitation; geometric models for Particle Physics; Supergravity and Supersymmetric Field Theories; Classical and Quantum Field Theory (also quantization over curved backgrounds); Gauge Theories; Topological Field Theories; Strings, Branes and Extended Objects Theory; Holography; Quantum Gravity, Loop Quantum Gravity and Quantum Cosmology; applications of Quantum Groups; Quantum Computation; Control Theory; Geometry of Chaos.