Relevant bibliographies by topics / Dirac operator

Academic literature on the topic 'Dirac operator'

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Published: 4 June 2021
Last updated: 8 June 2024

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Journal articles on the topic "Dirac operator"

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Patra, Rashmirekha, and Nihar Ranjan Satapathy. "Novel finite difference approach to discretize the symplectic dirac operator." Annals of Mathematics and Computer Science 18 (October 1, 2023): 90–103. http://dx.doi.org/10.56947/amcs.v18.211.

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Symplectic Dirac operator is an intertwining differential operator. Discretising symplectic Dirac operator gives a new direction to study the quantum space. The construction of discrete symplectic Dirac operator requires the theory of discrete symplectic Clifford analysis or the concept of discrete symplectic connections, which are not explained in literature. In this work, a discretization approach for symplectic Dirac operator is suggested by considering the forward and backward basis vectors on symplectic Clifford algebra. The suggested discrete symplectic Dirac operator is Ds=Ds++Ds- where the Ds+ and Ds- are the forward and backward discrete symplectic Dirac operators, respectively. The new discrete symplectic Dirac operator gives the factorization of discrete Laplacian on symplectic spaces. Further, we establish commutation relations involving forward and backward discrete symplectic Dirac operators in the representation theory.
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AVRAMIDI, IVAN G. "DIRAC OPERATOR IN MATRIX GEOMETRY." International Journal of Geometric Methods in Modern Physics 02, no. 02 (April 2005): 227–64. http://dx.doi.org/10.1142/s0219887805000636.

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We review the construction of the Dirac operator and its properties in Riemannian geometry, and show how the asymptotic expansion of the trace of the heat kernel determines the spectral invariants of the Dirac operator and its index. We also point out that the Einstein–Hilbert functional can be obtained as a linear combination of the first two spectral invariants of the Dirac operator. Next, we report on our previous attempts to generalize the notion of the Dirac operator to the case of Matrix Geometry, where, instead of a Riemannian metric there is a matrix valued self-adjoint symmetric two-tensor that plays a role of a "non-commutative" metric. We construct invariant first-order and second-order self-adjoint elliptic partial differential operators, which can be called "non-commutative" Dirac operators and non-commutative Laplace operators. We construct the corresponding heat kernel for the non-commutative Laplace type operator and compute its first two spectral invariants. A linear combination of these two spectral invariants gives a functional that can be considered as a non-commutative generalization of the Einstein–Hilbert action.
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Yuan, 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.

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The perturbed Dirac operators yield a factorization for the well-known Helmholtz equation. In this paper, using the fundamental solution for the perturbed Dirac operator, we define Cauchy-type integral operators (singular integral operators with a Cauchy kernel). With the help of these operators, we investigate generalized Riemann and Dirichlet problems for the perturbed Dirac equation which is a higher-dimensional generalization of a Vekua-type equation. Furthermore, applying the generalized Cauchy-type integral operator F˜λ, we construct the Mann iterative sequence and prove that the iterative sequence strongly converges to the fixed point of operator F˜λ.
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MATSUTANI, SHIGEKI. "DIRAC OPERATOR ON A CONFORMAL SURFACE IMMERSED IN ℝ4: A WAY TO FURTHER GENERALIZED WEIERSTRASS EQUATION." Reviews in Mathematical Physics 12, no. 03 (March 2000): 431–44. http://dx.doi.org/10.1142/s0129055x00000149.

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In the previous report (J. Phys.A30 (1997) 4019–4029), I showed that the Dirac operator defined over a conformal surface immersed in ℝ3 by means of confinement procedure is identified with the differential operator of the generalized Weierstrass equation and the Lax operator of the modified Novikov–Veselov (MNV) equation. In this article, using the same procedure, I determine the Dirac operator defined over a conformal surface immersed in ℝ4, which is for a Dirac field confined in the surface. Then it is reduced to the Lax operators of the nonlinear Schrödinger and the MNV equations by taking appropriate limits. It means that the Dirac operator is related to the further generalized Weierstrass equation for a surface in ℝ4.
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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.

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DABROWSKI, 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.

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We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle [Formula: see text].
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KHACHIDZE, TAMARI T., and ANZOR A. KHELASHVILI. "AN "ACCIDENTAL" SYMMETRY OPERATOR FOR THE DIRAC EQUATION IN THE COULOMB POTENTIAL." Modern Physics Letters A 20, no. 30 (September 28, 2005): 2277–81. http://dx.doi.org/10.1142/s0217732305018505.

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On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann operator and is closely connected to the familiar Laplace–Runge–Lenz vector. Our approach guarantees not only derivation of Johnson–Lippmann operator, but simultaneously commutativity with the Dirac Hamiltonian.
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Henheik, Joscha, and Roderich Tumulka. "Interior-boundary conditions for the Dirac equation at point sources in three dimensions." Journal of Mathematical Physics 63, no. 12 (December 1, 2022): 122302. http://dx.doi.org/10.1063/5.0104675.

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A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential.
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TANIŞLI, MURAT, MUSTAFA EMRE KANSU, and SÜLEYMAN DEMİR. "SUPERSYMMETRIC QUANTUM MECHANICS AND EUCLIDEAN–DIRAC OPERATOR WITH COMPLEXIFIED QUATERNIONS." Modern Physics Letters A 28, no. 08 (March 12, 2013): 1350026. http://dx.doi.org/10.1142/s0217732313500260.

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We propose an alternative formulation of the supersymmetric quantum mechanics and Euclidean Dirac and Dirac–Yang–Mills (DYM) operators in terms of complexified quaternions. 4×4 matrix representations of the complexified quaternions are used to express the Euclidean–Dirac operator and Yang–Mills gauge field.
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Aastrup, Johannes, and Jesper Møller Grimstrup. "The quantum holonomy-diffeomorphism algebra and quantum gravity." International Journal of Modern Physics A 31, no. 10 (April 6, 2016): 1650048. http://dx.doi.org/10.1142/s0217751x16500482.

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We introduce the quantum holonomy-diffeomorphism ∗-algebra, which is generated by holonomy-diffeomorphisms on a three-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Furthermore, we show that semiclassical states exist on the holonomy-diffeomorphism part of the algebra but that these states cannot be extended to the full algebra. Via a Dirac-type operator we derive a certain class of unbounded operators that act in the GNS construction of the semiclassical states. These unbounded operators are the type of operators, which we have previously shown to entail the spatial three-dimensional Dirac operator and Dirac–Hamiltonian in a semiclassical limit. Finally, we show that the structure of the Hamilton constraint emerges from a Yang–Mills-type operator over the space of SU(2)-connections.
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Dissertations / Theses on the topic "Dirac operator"

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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.

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This thesis consists of a summary of four papers dealing with resonances of Dirac operators on Euclidean 3-space. In Paper I we show that the Complex Absorbing Potential (CAP) method is valid in the semiclassical limit for resonances sufficiently close to the real line if the potential is smooth and compactly supported. In Paper II  we continue the investigations initiated in Paper I but here we study clouds of resonances close to the real line and show that in some sense the CAP method remains valid also for multiple resonances. In Paper III we study perturbations of Dirac operators with smooth decaying scalar potentials  and show that these possess many resonances near certain points related to the maximum and the minimum of the potential. In Paper IV we show a trace formula of Poisson type for Dirac operators having compactly supported potentials which is related to resonances. The techniques mainly stem from complex function theory and scattering theory.
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Bär, Christian. "Das Spektrum von Dirac-Operatoren." Bonn : [s.n.], 1991. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=003506032&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Kim, Yonne Mi. "Unique continuation theorems for the Dirac operator and the Laplace operator." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14469.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1989.
Title as it appeared in M.I.T. Graduate List, Feb. 1989: Carleman inequalities and strong unique continuation.
Includes bibliographical references (leaf 59).
by Yonne Mi Kim.
Ph.D.
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Thumstädter, Torsten. "Parameteruntersuchungen an Dirac-Modellen." [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10633955.

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Dumais, Guy. "Killing spinors and spectral properties of the Dirac operator." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=55442.

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A survey of the spectral properties of the classical Dirac operator on a Riemannian spin manifold is made. Killing spinors, which are special eigenfunctions of the Dirac operator, are studied and necessary conditions for their existence are given. Killing spinors on $ IR sp{n}$, $S sp{n}$ and $H sp{n}$ are also computed explicitly. Finally the transformation law for Dirac operator under conformal change of the metric is computed and a lower bound for the eigenvalues is given.
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Andersson, Linnéa. "Linear-scaling recursive expansion of the Fermi-Dirac operator." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-382829.

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Stadtmüller, Christoph Martin. "Horizontal Dirac Operators in CR Geometry." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18130.

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In dieser Dissertation beschäftigen wir uns mit angepassten Zusammenhängen und ihren (horizontalen) Dirac-Operatoren auf strikt pseudokonvexen CR-Mannigfaltigkeiten. Einen Zusammenhang nennen wir dann angepasst, wenn er die relevanten Daten parallelisiert. Wir beschreiben den Raum der angepassten Zusammenhänge, indem wir ihre Torsionstensoren studieren, von denen gewisse Teile durch die Geometrie der Mannigfaltigkeit festgelegt sind, während andere frei wählbar sind. Als Anwendung betrachten wir die Eigenschaften der Dirac-Operatoren, die zu diesen Zusammenhängen gehören. Weiter betrachten wir horizontale Dirac-Operatoren, die nur in Richtung des horizontalen Bündels H ableiten. Diese Operatoren sind besser an die Sub-Riemannsche Struktur einer CR-Mannigfaltigkeit angepasst als die vollen Dirac-Operatoren. Wir diskutieren, wann diese Operatoren formal selbstadjungiert sind und beweisen eine Weitzenböck-Typ-Formel. Wir konzentrieren uns dann auf den horizontalen Dirac-Operator zum Tanaka-Webster-Zusammenhang. Dieser ändert sich konform kovariant, wenn wir die Kontaktform konform ändern. Für diesen Operator betrachten wir weiterhin zwei Beispiele: Wir betrachten S^1-Bündel über Kähler-Mannigfaltigkeiten, insbesondere berechnen wir für Sphären einen Teil des Spektrums. Außerdem betrachten wir kompakte Quotienten der Heisenberggruppe und berechnen hier in den Dimensionen 3 und 5 das volle Spektrum. Die horizontalen Dirac-Operatoren sind nicht mehr elliptisch, sondern „elliptisch in Richtung von H“. Mithilfe des Heisenbergkalküls stellen wir fest, dass die horizontalen Dirac-Operatoren nicht hypoelliptisch sind. Im Fall des Tanaka-Webster-Zusammenhangs lässt sich aber zeigen, dass der zugehörige Operator auf gewissen Teilen des Spinorbündels hypoelliptisch ist. Dies genügt, um zu beweisen, dass er (nun auf dem gesamten Spinorbündel) ein reines Punktspektrum hat und die Eigenräume, bis auf den Kern, endlich-dimensional sind und aus glatten Eigenspinoren bestehen.
In 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.
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Richert, Manfred. "Streutheorie für Diracsche Aussenraumaufgaben." Bonn : [Math.-Naturwiss. Fak. der Univ.], 1992. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=005421124&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Hachem, Ghias. "Théorie spectrale de l'opérateur de Dirac avec un potentiel électromagnétique à croissance linéaire à l'infini." Paris 13, 1988. http://www.theses.fr/1988PA132008.

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L'objet de cette thèse est la théorie spectrale de l'opérateur de Dirac associé à un champ électrique extérieur. Notre approche est celle de la théorie de la diffusion. Dans un premier temps on étudie l'opérateur non perturbe dont le potentiel est une fonction linéaire d'une variable (champ électrique constant). On construit alors les fonctions propres généralisées de cet opérateur, pour cela on étudie une équation différentielle du second ordre dépendant d'un paramètre. On donne ensuite des estimations pour les fonctions propres généralisées et le théorème d'absorption limite. Dans la deuxième partie on étudie les perturbations de cet opérateur de base par des potentiels de courte portée, on donne une description du spectre de ces opérateurs, on obtient la représentation spectrale de ces opérateurs ainsi que des estimations montrant la décroissance dans le temps des états de diffusion.
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Jakubassa-Amundsen, Doris. "Spectral Theory of the Atomic Dirac Operator in the No-Pair Formalism." Diss., lmu, 2004. http://nbn-resolving.de/urn:nbn:de:bvb:19-23824.

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Books on the topic "Dirac operator"

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service), SpringerLink (Online, ed. The Dirac spectrum. Berlin: Springer, 2009.

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Delanghe, Richard. Clifford algebra and spinor-valued functions: A function theory for the Dirac operator. Dordrecht: Kluwer Academic Publishers, 1992.

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The heat kernel Lefschetz fixed point formula for the spin-c dirac operator. Boston: Birkhauser, 1996.

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Duistermaat, J. J. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Boston, MA: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8247-7.

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Duistermaat, J. J. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-5344-0.

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service), SpringerLink (Online, ed. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Boston, MA: Springer Science+Business Media, LLC, 2011.

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V, Tyutin I., Voronov B. L, and SpringerLink (Online service), eds. Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials. Boston: Birkhäuser Boston, 2012.

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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.

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S, Sargsi͡a︡n I., ed. Sturm-Liouville and Dirac operators. Dordrecht: Kluwer Academic, 1991.

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Berline, 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.

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Book chapters on the topic "Dirac operator"

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Martin, 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.

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Edmunds, David E., and W. Desmond Evans. "The Dirac Operator." In Springer Monographs in Mathematics, 281–301. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02125-2_12.

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Neuberger, Herbert. "The Overlap Dirac Operator." In Lecture Notes in Computational Science and Engineering, 1–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-58333-9_1.

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Bernstein, Swanhild. "A Fractional Dirac Operator." In Noncommutative Analysis, Operator Theory and Applications, 27–41. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29116-1_2.

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Duistermaat, J. J. "The Dolbeault-Dirac Operator." In The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator, 7–17. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-5344-0_2.

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Duistermaat, J. J. "The Dolbeault-Dirac Operator." In The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator, 7–17. Boston, MA: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8247-7_2.

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Kostant, Bertram. "Dirac Cohomology for the Cubic Dirac Operator." In Studies in Memory of Issai Schur, 69–93. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0045-1_4.

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Kostant, Bertram. "Dirac Cohomology for the Cubic Dirac Operator." In Collected Papers, 13–37. New York, NY: Springer New York, 2022. http://dx.doi.org/10.1007/978-0-387-09591-2_2.

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Kanazawa, Takuya. "Dirac Operator in Dense QCD." In Dirac Spectra in Dense QCD, 51–99. Tokyo: Springer Japan, 2012. http://dx.doi.org/10.1007/978-4-431-54165-3_3.

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Meinrenken, Eckhard. "as a geometric Dirac operator." In Clifford Algebras and Lie Theory, 219–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36216-3_9.

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Conference papers on the topic "Dirac operator"

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Korotyaev, Evgeny L., and Dmitrii S. Mokeev. "Dislocation problem for the Dirac operator." In 2019 Days on Diffraction (DD). IEEE, 2019. http://dx.doi.org/10.1109/dd46733.2019.9016424.

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Boitsev, A. A. "Boundary triplets approach for Dirac operator." In QMath12 – Mathematical Results in Quantum Mechanics. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814618144_0015.

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Kukushkin, Andrey A. "On homogenization of the periodic Dirac operator." In Days on Diffraction 2012 (DD). IEEE, 2012. http://dx.doi.org/10.1109/dd.2012.6402772.

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Baaske, Franka, and Swanhild Bernstein. "Scattering theory for a Dirac type operator." In 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4765467.

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Falomir, H. "Global boundary conditions for the Dirac operator." In Trends in theoretical physics CERN-Santiago de Compostela-La Plata meeting. AIP, 1998. http://dx.doi.org/10.1063/1.54693.

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Di Renzo, Francesco, and M. Brambilla. "The Dirac operator spectrum: a perturbative approach." In The XXVII International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2010. http://dx.doi.org/10.22323/1.091.0209.

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Damiano, Alberto, Vladimír Souček, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Dirac Operator in Several Variables and Combinatorial Identities." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790256.

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Krýsl, Svatopluk. "Symplectic Dirac Operator and its Higher Spin Analogues." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991017.

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Sprössig, Wolfgang, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Exponentials of the Dirac Operator and an Application." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241598.

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Calmon, Lucille, Michael T. Schaub, and Ginestra Bianconi. "Higher-order signal processing with the Dirac operator." In 2022 56th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2022. http://dx.doi.org/10.1109/ieeeconf56349.2022.10052062.

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Reports on the topic "Dirac operator"

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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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Spanier, Stefane. Operation of the Cherenkov Detector DIRC of BaBar at High Luminosity. Office of Scientific and Technical Information (OSTI), March 2001. http://dx.doi.org/10.2172/784888.

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