Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 18 of 18 for “"Dirac operator"”.
-
Unique continuation theorems for the Dirac operator and the Laplace operator
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1989.
-
Spectral Theory of the Atomic Dirac Operator in the No-Pair Formalism
… einer unitaeren Transformation wird der Coulomb-Dirac-Operator eines Ions in einen pseudorelativistischen Operator uebergefuehrt, der zu beliebiger Ordnung n in der Potentialstaerke block-diagonal ist bezueglich der Projektionen auf den positiven bzw. negativen Spektralraum des freien …
-
Results on the number of zero modes of the Weyl-Dirac operator
… magnetic potential A one can define the Weyl-Dirac operator σ·(−i∇−A) on R 3 . An L 2 eigenfunction of σ · (−i∇ − A) corresponding to 0 is called a zero mode. In this thesis we will be concerned with the zero mode problem for the WeylDirac operator and some related problems. The main results …
-
L2-Indices for Perturbed Dirac Operators on Odd Dimensional Open Complete Manifolds
… and Anghel type the L2-index of the perturbed Dirac operator on a Spin c -manifold is realized as the result of pairing an element in K -homology with an element of compactly supported K -cohomology. This is achieved by putting the problem of calculating the Fredholm index of the perturbed …
-
Spectral asymptotics for coupled Dirac operators
… asymptotic spectral flow for a family of coupled Dirac operators. We prove that the leading order term in the spectral flow on an n dimensional manifold is of order r n+1/2 followed by a remainder of O(r n/2). We perform computations of spectral flow on the sphere which show that O(r n-1/2) is the …
-
Ricci Curvature of Noncommutative Three Tori, Entropy, and Second Quantization
… mathcal{H},D)$, where $D$ plays the role of the Dirac operator acting on the Hilbert space of spinors. Ideas of spectral geometry can then be used to define suitable notions such as volume, scalar curvature, and Ricci curvature. In particular, one can construct the Ricci curvature from the …
-
Gluing Z₂-Harmonic Spinors on 3-Manifolds
… analysis of degenerating families of elliptic operators. Part II: This part studies the deformation theory of Z₂-harmonic spinors. For a fixed smooth singular set, the deformation theory of 𝑍₂-harmonic spinors is obstructed by infinite-dimensional cokernel of the semi-Fredholm Z₂-Dirac …
-
Eta-invariants and Molien series for unimodular group
… the way computations of the spectrum of the Dirac operator on the sphere are performed.
-
Dirac operators and monopoles with singularities
… of the thesis, we prove an index theorem for Dirac operators of conic singularities with codimension 2. One immediate corollary is the generalized Rohklin congruence formula. The eta function for a twisted spin Dirac operator on a circle bundle over a even dimensional spin manifold is also …
-
Fermions in Yang-Mills gauge theories: invariance, covariance and topology
… the invariance and covariance properties of the Dirac operator describing fermions in Yang-Mills fields. This includes the study of anomalies of the gauge currents. We are particularly interested in the geometric and topological features in the problem. The complicated topological structures and …
-
Finite Dimensional Approximation and Pin(2)-equivariant Property for Rarita-Schwinger-Seiberg-Witten Equations
<p>The Rarita-Schwinger operator Q was initially proposed in the 1941 paper by Rarita and Schwinger to study wave functions of particles of spin 3/2, and there is a vast amount of physics literature on its properties. Roughly speaking, 3/2−spinors are spinor-valued 1-forms that also happen to be in …
-
Ground state and thermal dynamics of strong interaction
… vacuum sector, we compute the spectrum of the Dirac operator. The flow equations are generalized to finite temperatures and densities via the Matsubara formalism. Within this scheme, we analyze the chiral phase diagram and the equation of state of quark matter and compare our results to recent …
-
Conformally Invariant Operators in Higher Spin Spaces
… arbitrary order conformally invariant operators in higher spin spaces, where functions take values in irreducible representations of Spin groups. We provide explicit formulas for them.</p> <p>We first construct the Dirac operator and Rarita-Schwinger operator as Stein Weiss type …
-
Multi-dimensional continuous wavelet transforms and generalized fourier transforms in Clifford analysis
… functions, are null-solutions of the so-called Dirac operator, a first order rotationally invariant differential operator factorizing the Laplacian in higher dimensions. This factorization of the Laplace operator establishes a special relationship between monogenic functions and harmonic …
-
The Ricci Flow on Spin Manifolds
… properties of the naturally associated weighted Dirac operator, introduced by Perelman, and its relationship with the weighted scalar curvature are investigated. Further, a generalization of the ADM mass for weighted asymptotically Euclidean (AE) manifolds is defined; on manifolds with …
-
Characteristic polynomials of random matrices and their role in an effective theory of strong interactions
… only the smallest eigenvalues of the QCD Dirac operator. We consider four members of the chGUE(N) symmetry class: the classical chGUE(N) consisting of Hermitian, chiral block matrices with complex entries and its extensions by N_f massive flavors describing dynamical quarks. Furthermore, …
-
On a pseudodifferential calculus with modest boundary decay condition
… mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators …