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Showing 1 to 15 of 15 for “"Dirac Operators"”.
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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 …
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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 …
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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 …
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Spectral properties of Spin^c Dirac operators on $T^3$, $S^1 × S^2$ and $S^3$
… Spektrum und Eigenbasen für verschiedene Spin^c-Dirac-Operatoren auf den drei im Titel genannten Mannigfaltigkeiten. Weiterhin betrachten wir Familien von Spin^c-Dirac-Operatoren und untersuchen ihre spektralen Eigenschaften mit Hilfe von spektralen Schnitten. Dabei sind wir besonders an …
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Analytic aspects of periodic instantons
… quotients of R⁴. The Fredholm theory of twisted Dirac operators on cylindrical manifolds is derived, the spectra of spin Dirac operators on spheres and on product manifolds are computed. A brief discussion on the decay of spatially-periodic and doubly-periodic instantons is included.
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Positive scalar curvature and Callias-type index theorems for proper actions
… is a study of the equivariant index theory of Dirac operators and Callias-type operators in two distinct settings, namely on cocompact and non-cocompact manifolds with a Lie group action. The first two chapters are a short resumé of Dirac operators and index theory and form a common …
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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 …
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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 …
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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 …
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Extensions of the theory of tent spaces and applications to boundary value problems
… and Besov spaces adapted to perturbed Dirac operators. These spaces play a key role in the classification of solutions to first-order Cauchy–Riemann systems (or equivalently, the classification of conormal gradients of solutions to second-order elliptic systems) within weighted tent …
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Extensions of the theory of tent spaces and applications to boundary value problems
… and Besov spaces adapted to perturbed Dirac operators. These spaces play a key role in the classification of solutions to first-order Cauchy–Riemann systems (or equivalently, the classification of conormal gradients of solutions to second-order elliptic systems) within weighted tent …
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Mathematical Aspects of Field Theory: Nahm's Equations and Jacobi Forms
… on Nahm's equations that correspond to the Dirac multimonopole in Yang-Mills theory. The algebro-geometric integration method is to construct solutions via a linear flow in the Jacobian of the spectral curve associated to the Lax pair. We construct a frame of sections of this linear flow, …
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Physics on Noncommutative Spacetimes
… systems on the fuzzy sphere. The construction of Dirac and chirality operators for an arbitrary spin<em> j</em> is studied on both S<sup><sub>2</sub></sup>/F and S<sup>2</sup> in detail. We compute the spectrums of the spin 1 and spin 3/2 Dirac operators on S<sup><sub>2</sub></sup>/F. These …
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Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms