Academic literature on the topic 'Dirac Operators'
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Journal articles on the topic "Dirac Operators"
Cojuhari, Petru, and Aurelian Gheondea. "Embeddings, Operator Ranges, and Dirac Operators." Complex Analysis and Operator Theory 5, no. 3 (April 13, 2010): 941–53. http://dx.doi.org/10.1007/s11785-010-0066-5.
Full textAshrafyan, Yuri, and Tigran Harutyunyan. "Isospectral Dirac operators." Electronic Journal of Qualitative Theory of Differential Equations, no. 4 (2017): 1–9. http://dx.doi.org/10.14232/ejqtde.2017.1.4.
Full textNolder, Craig A., and John Ryan. "p-Dirac Operators." Advances in Applied Clifford Algebras 19, no. 2 (March 19, 2009): 391–402. http://dx.doi.org/10.1007/s00006-009-0162-7.
Full textNotte-Cuello, E. A. "On the Dirac and Spin-Dirac Operators." Advances in Applied Clifford Algebras 20, no. 3-4 (May 11, 2010): 765–80. http://dx.doi.org/10.1007/s00006-010-0220-1.
Full textProkhorenkov, Igor, and Ken Richardson. "Perturbations of Dirac operators." Journal of Geometry and Physics 57, no. 1 (December 2006): 297–321. http://dx.doi.org/10.1016/j.geomphys.2006.03.004.
Full textRyan, John. "Intrinsic Dirac Operators inCn." Advances in Mathematics 118, no. 1 (March 1996): 99–133. http://dx.doi.org/10.1006/aima.1996.0019.
Full textBRIHAYE, Y., and A. NININAHAZWE. "DIRAC OSCILLATORS AND QUASI-EXACTLY SOLVABLE OPERATORS." Modern Physics Letters A 20, no. 25 (August 20, 2005): 1875–85. http://dx.doi.org/10.1142/s0217732305018128.
Full textBaum, Paul F., and Erik van Erp. "K-homology and Fredholm operators I: Dirac operators." Journal of Geometry and Physics 134 (December 2018): 101–18. http://dx.doi.org/10.1016/j.geomphys.2018.08.008.
Full textYuan, Hongfen, Guohong Shi, and Xiushen Hu. "Boundary Value Problems for the Perturbed Dirac Equation." Axioms 13, no. 4 (April 4, 2024): 238. http://dx.doi.org/10.3390/axioms13040238.
Full textDABROWSKI, LUDWIK, ANDRZEJ SITARZ, and ALESSANDRO ZUCCA. "DIRAC OPERATORS ON NONCOMMUTATIVE PRINCIPAL CIRCLE BUNDLES." International Journal of Geometric Methods in Modern Physics 11, no. 01 (December 16, 2013): 1450012. http://dx.doi.org/10.1142/s0219887814500121.
Full textDissertations / Theses on the topic "Dirac Operators"
Kungsman, Jimmy. "Resonances of Dirac Operators." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-223841.
Full textGinoux, Nicolas. "Dirac operators on Lagrangian submanifolds." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2005/562/.
Full textYang, Fangyun Ph D. Massachusetts Institute of Technology. "Dirac operators and monopoles with singularities." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/41723.
Full textIncludes bibliographical references (p. 75-77).
This thesis consists of two parts. In the first part 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 derived along the way. In the second part, we study the moduli space of monopoles with singularities along an embedded surface. We prove that when the base manifold is Kahler, there is a holomorphic description of the singular monopoles. The compactness for this case is also proved.
by Fangyun Yang.
Ph.D.
Savale, Nikhil Jr (Nikhil A. ). "Spectral asymptotics for coupled Dirac operators." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/77804.
Full textCataloged from PDF version of thesis.
Includes bibliographical references (p. 137-139).
In this thesis, we study the problem of 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 best possible estimate on the remainder. To obtain the sharp remainder we study a semiclassical Dirac operator and show that its odd functional trace exhibits cancellations in its first n+3/2 terms. A normal form result for this Dirac operator and a bound on its counting function are also obtained.
by Nikhil Savale.
Ph.D.
Stadtmüller, Christoph Martin. "Horizontal Dirac Operators in CR Geometry." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18130.
Full textIn the present thesis, we study adapted connections and their (horizontal) Dirac operators on strictly pseudoconvex CR manifolds. An adapted connection is one that parallelises the relevant data. We describe the space of adapted connections through their torsion tensors, certain parts of which are determined by the geometry of the manifold, while others may be freely chosen. As an application, we study the properties of the Dirac operators induced by these connections. We further consider horizontal Dirac operators, which only derive in the direction of the horizontal bundle H. These operators are more adapted to the essentially sub-Riemannian structure of a CR manifold than the full Dirac operators. We discuss the question of their self-adjointness and prove a Weitzenböck type formula for these operators. Focusing on the horizontal Dirac operator associated with the Tanaka-Webster connection, we show that this operator changes in a covariant way if we change the contact form conformally. Moreover, for this operator we discuss two examples: On S^1-bundles over Kähler manifolds, we can compute part of the spectrum and for compact quotients of the Heisenberg group, we determine the whole spectrum in dimensions three and five. The horizontal Dirac operators are not elliptic, but rather "elliptic in some directions". We review the Heisenberg Calculus for such operators and find that in general, the horizontal Dirac operators are not hypoelliptic. However, in the case of the Tanaka-Webster connection, the associated horizontal Dirac operator is hypoelliptic on certain parts of the spinor bundle and this is enough to prove that its spectrum consists only of eigenvalues and except for the kernel, the corresponding eigenspaces are finite-dimensional spaces of smooth sections.
Anghel, Nicolae. "L²-index theorems for perturbed Dirac operators /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487598303839391.
Full textAfentoulidis-Almpanis, Spyridon. "Noncubic Dirac Operators for finite-dimensional modules." Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0035.
Full textThis thesis focuses on the study of noncubic Dirac operators within the framework of representation theory of Lie groups. After recalling basic notions of Lie theory and Clifford algebras, we present the main properties of cubic Dirac operators D introduced by Kostant in 1999. These results quickly aroused great interest. In particular, in the late 1990’s, Vogan introduced a cohomology defined by Kostant operator D and suggested a cohomological classification of representations. Dirac cohomology was computed for various families of representations, such as the discrete series, Aq(>) modules or finite dimensional representations. It turns out that for finite dimensional modules, Dirac cohomology coincides with the kernel of D. It appears that Kostant’s Dirac operator is an algebraic version of a specific member of a continuous family of geometric Dirac operators introduced by Slebarski in the mid 1980’s in the context of bundles over homogeneous spaces G/H of compact groups. What distinguishes the cubic Dirac operator is that it is the only member of this family whose square, generalizing Parthasarathy’s formula, differs from the Casimir operator up to a scalar. This property has important applications in representation theory of Lie groups. The square of the noncubic Dirac operators, i.e. of the other members of Slebarski’s family, was calculated by Agricola who also established precise links between these noncubic operators and string theory in physics. Actually, noncubic Dirac operators are invariant differential operators, and therefore their kernels define (finite-dimensional) representations of compact groups. In this thesis we study the kernel of noncubic Dirac operators, and we show that, under certain conditions on the homogeneous spaces G/H, the kernel contains the kernel of the cubic Dirac operator. We obtain an explicit formula for the kernel which we apply to the case of classical Lie algebras and of exceptional Lie algebras. We remark that some properties of noncubic operators are analogous to those of Kostant cubic Dirac operator, such as the index. We also deduce some observations on noncubic geometric Dirac operators
Zucca, Alessandro. "Dirac Operators on Quantum Principal G-Bundles." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4108.
Full textNita, A. "Essential Self-Adjointness of the Symplectic Dirac Operators." Thesis, University of Colorado at Boulder, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10108819.
Full textThe main problem we consider in this thesis is the essential self-adjointness of the symplectic Dirac operators D and D constructed by Katharina Habermann in the mid 1990s. Her constructions run parallel to those of the well-known Riemannian Dirac operators, and show that in the symplectic setting many of the same properties hold. For example, the symplectic Dirac operators are also unbounded and symmetric, as in the Riemannian case, with one important difference: the bundle of symplectic spinors is now infinite-dimensional, and in fact a Hilbert bundle. This infinite dimensionality makes the classical proofs of essential self-adjointness fail at a crucial step, namely in local coordinates the coefficients are now seen to be unbounded operators on L2(Rn). A new approach is needed, and that is the content of these notes. We use the decomposition of the spinor bundle into countably many finite-dimensional subbundles, the eigenbundles of the harmonic oscillator, along with the simple behavior of D and D with respect to this decomposition, to construct an inductive argument for their essential self-adjointness. This requires the use of ancillary operators, constructed out of the symplectic Dirac operators, whose behavior with respect to the decomposition is transparent. By an analysis of their kernels we manage to deduce the main result one eigensection at a time.
Zreik, Mahdi. "Spectral properties of Dirac operators on certain domains." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0085.
Full textThis thesis mainly focused on the spectral analysis of perturbation models of the free Dirac operator, in 2-D and 3-D space.The first chapter of this thesis examines perturbation of the Dirac operator by a large mass M, supported on a domain. Our main objective is to establish, under the condition of sufficiently large mass M, the convergence of the perturbed operator, towards the Dirac operator with the MIT bag condition, in the norm resolvent sense. To this end, we introduce what we refer to the Poincaré-Steklov (PS) operators (as an analogue of the Dirichlet-to-Neumann operators for the Laplace operator) and analyze them from the microlocal point of view, in order to understand precisely the convergence rate of the resolvent. On one hand, we show that the PS operators fit into the framework of pseudodifferential operators and we determine their principal symbols. On the other hand, since we are mainly concerned with large masses, we treat our problem from the semiclassical point of view, where the semiclassical parameter is h = M^{-1}. Finally, by establishing a Krein formula relating the resolvent of the perturbed operator to that of the MIT bag operator, and using the pseudodifferential properties of the PS operators combined with the matrix structures of the principal symbols, we establish the required convergence with a convergence rate of mathcal{O}(M^{-1}).In the second chapter, we define a tubular neighborhood of the boundary of a given regular domain. We consider perturbation of the free Dirac operator by a large mass M, within this neighborhood of thickness varepsilon:=M^{-1}. Our primary objective is to study the convergence of the perturbed Dirac operator when M tends to +infty. Comparing with the first part, we get here two MIT bag limit operators, which act outside the boundary. It's worth noting that the decoupling of these two MIT bag operators can be considered as the confining version of the Lorentz scalar delta interaction of Dirac operator, supported on a closed surface. The methodology followed, as in the previous problem study the pseudodifferential properties of Poincaré-Steklov operators. However, the novelty in this problem lies in the control of these operators by tracking the dependence on the parameter varepsilon, and consequently, in the convergence as varepsilon goes to 0 and M goes to +infty. With these ingredients, we prove that the perturbed operator converges in the norm resolvent sense to the Dirac operator coupled with Lorentz scalar delta-shell interaction.In the third chapter, we investigate the generalization of an approximation of the three-dimensional Dirac operator coupled with a singular combination of electrostatic and Lorentz scalar delta-interactions supported on a closed surface, by a Dirac operator with a regular potential localized in a thin layer containing the surface. In the non-critical and non-confining cases, we show that the regular perturbed Dirac operator converges in the strong resolvent sense to the singular delta-interaction of the Dirac operator. Moreover, we deduce that the coupling constants of the limit operator depend nonlinearly on those of the potential under consideration.In the last chapter, our study focuses on the two-dimensional Dirac operator coupled with the electrostatic and Lorentz scalar delta-interactions. We treat in low regularity Sobolev spaces (H^{1/2}) the self-adjointness of certain realizations of these operators in various curve settings. The most important case in this chapter arises when the curves under consideration are curvilinear polygons, with smooth, differentiable edges and without cusps. Under certain conditions on the coupling constants, using the Fredholm property of certain boundary integral operators, and exploiting the explicit form of the Cauchy transform on non-smooth curves, we achieve the self-adjointness of the perturbed operator
Books on the topic "Dirac Operators"
1955-, Ryan John, Struppa Daniele Carlo 1955-, and International Society for Analysis, Applications, and Computation. Congress, eds. Dirac operators in analysis. Harlow, Essex, England: Longman, 1998.
Find full textS, Sargsi͡a︡n I., ed. Sturm-Liouville and Dirac operators. Dordrecht: Kluwer Academic, 1991.
Find full textBerline, Nicole, Ezra Getzler, and Michèle Vergne. Heat Kernels and Dirac Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-58088-8.
Full textLevitan, B. M., and I. S. Sargsjan. Sturm—Liouville and Dirac Operators. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3748-5.
Full textHabermann, Katharina, and Lutz Habermann. Introduction to Symplectic Dirac Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/b138212.
Full textDirac operators and spectral geometry. Cambridge: Cambridge University Press, 1998.
Find full textThomas, Friedrich. Dirac operators in Riemannian geometry. Providence, R.I: American Mathematical Society, 2000.
Find full textBooß-Bavnbek, Bernhelm, and Krzysztof P. Wojciechowski. Elliptic Boundary Problems for Dirac Operators. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0337-7.
Full textBook chapters on the topic "Dirac Operators"
Cnops, Jan. "Dirac Operators." In An Introduction to Dirac Operators on Manifolds, 61–89. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0065-9_3.
Full textBooß-Bavnbek, Bernhelm, and Krzysztof P. Wojciechowski. "Dirac Operators." In Elliptic Boundary Problems for Dirac Operators, 19–25. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0337-7_3.
Full textFriedrich, Thomas. "Dirac operators." In Graduate Studies in Mathematics, 57–90. Providence, Rhode Island: American Mathematical Society, 2000. http://dx.doi.org/10.1090/gsm/025/03.
Full textGesztesy, Fritz, and Marcus Waurick. "Dirac-Type Operators." In The Callias Index Formula Revisited, 55–63. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29977-8_6.
Full textMartin, Mircea. "Deconstructing Dirac operators. III: Dirac and semi-Dirac pairs." In Topics in Operator Theory, 347–62. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0161-0_14.
Full textBooß-Bavnbek, Bernhelm, and Krzysztof P. Wojciechowski. "Dirac Operators and Chirality." In Elliptic Boundary Problems for Dirac Operators, 40–42. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0337-7_7.
Full textCordes, H. O. "On Dirac Observables." In Semigroups of Operators: Theory and Applications, 61–77. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8417-4_6.
Full textBerline, Nicole, Ezra Getzler, and Michèle Vergne. "Clifford Modules and Dirac Operators." In Heat Kernels and Dirac Operators, 99–137. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-58088-8_4.
Full textBerline, Nicole, Ezra Getzler, and Michèle Vergne. "Index Density of Dirac Operators." In Heat Kernels and Dirac Operators, 139–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-58088-8_5.
Full textTuschmann, Wilderich, and David J. Wraith. "Dirac operators and index theorems." In Oberwolfach Seminars, 17–25. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0948-1_3.
Full textConference papers on the topic "Dirac Operators"
Arriola, E. Ruiz. "Anomalies for nonlocal dirac operators." In The international workshop on hadron physics of low energy QCD. AIP, 2000. http://dx.doi.org/10.1063/1.1303042.
Full textTantalo, Nazario. "A mass preconditioning for lattice Dirac operators." In The XXVIII International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.105.0041.
Full textMARTIN, MIRCEA. "DECONSTRUCTING DIRAC OPERATORS I: QUANTITATIVE HARTOGS-ROSENTHAL THEOREMS." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0102.
Full textBrackx, F., H. De Schepper, R. Lávička, V. Souček, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Fischer Decompositions of Kernels of Hermitean Dirac Operators." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498050.
Full textErcan, Ahu, and Etibar Panakhov. "Stability of the spectral problem for Dirac operators." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952082.
Full text"III.2 Dirac operators in analysis and related topics." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_others08.
Full textDe Schepper, H., D. Eelbode, T. Raeymaekers, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "On an Inductive Construction of Higher Spin Dirac Operators." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498058.
Full textMichel, Jean-Philippe. "Higher Symmetries of Laplace and Dirac operators - towards supersymmetries." In Frontiers of Fundamental Physics 14. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.224.0145.
Full textTOMODA, ATSUSHI. "A RELATION ON SPIN BUNDLE GERBES AND MAYER'S DIRAC OPERATORS." In Proceedings of the COE International Workshop. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812775061_0021.
Full textGattringer, Christof, and Stefan Solbrig. "Low-lying spectrum for lattice Dirac operators with twisted mass." In XXIIIrd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2005. http://dx.doi.org/10.22323/1.020.0127.
Full textReports on the topic "Dirac Operators"
Tolksdorf, Jurgen. Gauge Theories with Spontaneously Broken Gauge Symmetry, Connections and Dirac Operators. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-141-162.
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