Dirac operator

Part 1 of ebook "Introductory quantum mechanics: A traditional approach emphasizing connections with classical physics" provides readers with contents including: mathematical preliminaries; free-particle Schrödinger equation - wave packets; Schrödinger's equation with potential energy - introduction to operators; postulates and basic elements of quantum mechanics - properties of operators; simple harmonic oscillator - one dimension; problems in two and three-dimensions - general considerations;...

317p dangsovu 20-10-2023 7 3   Download

Part 1 of ebook "Mathematical physics: Applied mathematics for scientists and engineers" provides readers with contents including: Chapter 1 - A review of vector and matrix algebra using subscript/summation conventions; Chapter 2 - Differential and integral operations on vector and scalar fields; Chapter 3 - Curvilinear coordinate systems; Chapter 4 - Introduction to tensors; Chapter 5 - The dirac δ-function; Chapter 6 - Introduction to complex variables; Chapter 7 - Fourier series; Chapter 8 - Fourier transforms; Chapter 9 - Laplace transforms;...

353p lytamnguyet 04-08-2023 9 4   Download

Ebook "An Introduction to Quantum computing" provide readers with content about: introduction and background; linear algebra and the dirac notation; qubits and the framework of quantum mechanics; a quantum model of computation; superdense coding and quantum teleportation; introductory quantum algorithms; algorithms with superpolynomial speed-up;...

284p tieuduongchi 07-10-2022 11 5   Download

In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.

19p nutifooddau 21-01-2019 17 2   Download

In this paper, we write Seiberg–Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spinc-structure, we use the generalized Tanaka–Webster connection on a Spinc spinor bundle of a contact metric manifold to define the Dirac-type operators and write the Dirac equation.

7p danhdanh27 07-01-2019 24 2   Download

In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl’s limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular.

18p danhdanh27 07-01-2019 14 1   Download

In this paper we construct Weyl’s theory for the singular left-definite Dirac systems. In particular, we prove that there exists at least one solution of the system of equations that lies in the Sobolev space. Moreover, we describe the behavior of the solution belonging to the Sobolev space around the singular point.

7p danhdanh27 07-01-2019 17 1   Download

In this paper we extend the results obtained in [9], [10] to manifolds with SpinC -structures defined, near the boundary, by an almost complex structure. We show that on such a manifold with a strictly pseudoconvex boundary, there ¯ are modified ∂-Neumann boundary conditions defined by projection operators, Reo , which give subelliptic Fredholm problems for the SpinC -Dirac operator, + .eo . We introduce a generalization of Fredholm pairs to the “tame” category.

68p dontetvui 17-01-2013 64 8   Download

We assume that the manifold with boundary, X, has a SpinC -structure with spinor bundle S Along the boundary, this structure agrees with the /. structure defined by an infinite order, integrable, almost complex structure and the metric is K¨hler. In this case the SpinC -Dirac operator . agrees with a ¯ ¯ ∂ + ∂ ∗ along the boundary. The induced CR-structure on bX is integrable and either strictly pseudoconvex or strictly pseudoconcave. We assume that E → X is a complex vector bundle, which has an infinite order, integrable, complex structure along bX, compatible with that defined...

56p noel_noel 17-01-2013 44 6   Download

Let X be a compact K¨hler manifold with strictly pseudoconvex bounda ary, Y. In this setting, the SpinC Dirac operator is canonically identified with ¯ ¯ ∂ + ∂ ∗ : C ∞ (X; Λ0,e ) → C ∞ (X; Λ0,o ). We consider modifications of the classi¯ cal ∂-Neumann conditions that define Fredholm problems for the SpinC Dirac operator. In Part 2, [7], we use boundary layer methods to obtain subelliptic estimates for these boundary value problems. Using these results, we obtain an expression for the finite part of the holomorphic Euler characteristic of a strictly pseudoconvex manifold...

33p noel_noel 17-01-2013 42 5   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Tổng quát Dirac khai thác một số kỳ dị...

18p matuot_266 27-08-2011 41 2   Download