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Academic literature on the topic 'Twisted Dirac operators'

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Published: 14 March 2023

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Journal articles on the topic "Twisted Dirac operators"

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Nagase, Masayoshi. "Twistor spaces and the adiabatic limits of Dirac operators." Nagoya Mathematical Journal 164 (December 2001): 53–73. http://dx.doi.org/10.1017/s0027763000008035.

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We show that a (Spinq-style) twistor space admits a canonical Spin structure. The adiabatic limits of η-invariants of the associated Dirac operator and of an intrinsically twisted Dirac operator are then investigated.
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De Schepper, H., D. Eelbode, and T. Raeymaekers. "Twisted Higher Spin Dirac Operators." Complex Analysis and Operator Theory 8, no. 2 (March 24, 2013): 429–47. http://dx.doi.org/10.1007/s11785-013-0295-5.

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Sitarz, Andrzej. "Twisted Dirac operators over quantum spheres." Journal of Mathematical Physics 49, no. 3 (March 2008): 033509. http://dx.doi.org/10.1063/1.2842067.

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B�r, Christian. "Harmonic spinors for twisted Dirac operators." Mathematische Annalen 309, no. 2 (October 1, 1997): 225–46. http://dx.doi.org/10.1007/s002080050111.

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Homma, Yasushi. "Twisted Dirac operators and generalized gradients." Annals of Global Analysis and Geometry 50, no. 2 (March 3, 2016): 101–27. http://dx.doi.org/10.1007/s10455-016-9503-7.

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Wulff, Christopher. "Coarse indices of twisted operators." Journal of Topology and Analysis 11, no. 04 (December 2019): 823–73. http://dx.doi.org/10.1142/s179352531950033x.

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Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in [Formula: see text]-theory. The other type is by module multiplications in [Formula: see text]-theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Higson corona.
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Mehdi, S., and P. Pandžić. "Representation theoretic embedding of twisted Dirac operators." Representation Theory of the American Mathematical Society 25, no. 26 (September 20, 2021): 760–79. http://dx.doi.org/10.1090/ert/583.

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Let G G be a non-compact connected semisimple real Lie group with finite center. Suppose L L is a non-compact connected closed subgroup of G G acting transitively on a symmetric space G / H G/H such that L ∩ H L\cap H is compact. We study the action on L / L ∩ H L/L\cap H of a Dirac operator D G / H ( E ) D_{G/H}(E) acting on sections of an E E -twist of the spin bundle over G / H G/H . As a byproduct, in the case of ( G , H , L ) = ( S L ( 2 , R ) × S L ( 2 , R ) , Δ ( S L ( 2 , R ) × S L ( 2 , R ) ) , S L ( 2 , R ) × S O ( 2 ) ) (G,H,L)=(SL(2,{\mathbb R})\times SL(2,{\mathbb R}),\Delta (SL(2,{\mathbb R})\times SL(2,{\mathbb R})),SL(2,{\mathbb R})\times SO(2)) , we identify certain representations of L L which lie in the kernel of D G / H ( E ) D_{G/H}(E) .
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Wei, Sining, and Yong Wang. "Twisted dirac operators and Kastler-Kalau-Walze theorems for six-dimensional manifolds with boundary." International Journal of Geometric Methods in Modern Physics 17, no. 14 (November 7, 2020): 2050211. http://dx.doi.org/10.1142/s0219887820502114.

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In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.
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GINOUX, NICOLAS, and BERTRAND MOREL. "ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR." International Journal of Mathematics 13, no. 05 (July 2002): 533–48. http://dx.doi.org/10.1142/s0129167x0200140x.

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We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.
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Anghel, Nicolae. "Generic vanishing for harmonic spinors of twisted Dirac operators." Proceedings of the American Mathematical Society 124, no. 11 (1996): 3555–61. http://dx.doi.org/10.1090/s0002-9939-96-03475-2.

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Dissertations / Theses on the topic "Twisted Dirac operators"

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Buggisch, Lukas Werner [Verfasser], and Johannes [Akademischer Betreuer] Ebert. "The spectral flow theorem for families of twisted Dirac operators / Lukas Werner Buggisch ; Betreuer: Johannes Ebert." Münster : Universitäts- und Landesbibliothek Münster, 2019. http://d-nb.info/1190724960/34.

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Zhang, Dapeng. "Projective Dirac Operators, Twisted K-Theory, and Local Index Formula." Thesis, 2011. https://thesis.library.caltech.edu/6466/1/thesis_Dapeng_Zhang.pdf.

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We construct a canonical noncommutative spectral triple for every oriented closed Riemannian manifold, which represents the fundamental class in the twisted K-homology of the manifold. This so-called "projective spectral triple" is Morita equivalent to the well-known commutative spin spectral triple provided that the manifold is spin-c. We give an explicit local formula for the twisted Chern character for K-theories twisted with torsion classes, and with this formula we show that the twisted Chern character of the projective spectral triple is identical to the Poincare dual of the A-hat genus of the manifold.
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Holíková, Marie. "Symplektická spin geometrie." Doctoral thesis, 2016. http://www.nusl.cz/ntk/nusl-348950.

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The symplectic Dirac and the symplectic twistor operators are sym- plectic analogues of classical Dirac and twistor operators appearing in spin- Riemannian geometry. Our work concerns basic aspects of these two ope- rators. Namely, we determine the solution space of the symplectic twistor operator on the symplectic vector space of dimension 2n. It turns out that the solution space is a symplectic counterpart of the orthogonal situation. Moreover, we demonstrate on the example of 2n-dimensional tori the effect of dependence of the solution spaces of the symplectic Dirac and the symplectic twistor operators on the choice of the metaplectic structure. We construct a symplectic generalization of classical theta functions for the symplectic Dirac operator as well. We study several basic aspects of the symplectic version of Clifford analysis associated to the symplectic Dirac operator. Focusing mostly on the symplectic vector space of the real dimension 2, this amounts to the study of first order symmetry operators of the symplectic Dirac ope- rator, symplectic Clifford-Fourier transform and the reproducing kernel for the symplectic Fischer product including the construction of bases for the symplectic monogenics of the symplectic Dirac operator in real dimension 2 and their extension to symplectic spaces...
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Books on the topic "Twisted Dirac operators"

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Tsai, Chung-Jun. Asymptotic spectral flow for Dirac operators of disjoint Dehn twists. 2011.

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Book chapters on the topic "Twisted Dirac operators"

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Krähmer, Ulrich, and Elmar Wagner. "Twisted Dirac Operator on Quantum SU(2) in Disc Coordinates." In Operator Algebras, Toeplitz Operators and Related Topics, 233–53. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44651-2_16.

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Paradan, Paul-`Emile, and Mich`ele Vergne. "Equivariant Index of Twisted Dirac Operators and Semi-classical Limits." In Lie Groups, Geometry, and Representation Theory, 419–58. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02191-7_15.

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Raeymaekers, T. "Decomposition of the Twisted Dirac Operator." In Clifford Analysis and Related Topics, 97–111. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00049-3_6.

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Friedrich, Thomas. "Eigenvalue estimates for the Dirac operator and twistor spinors." In Graduate Studies in Mathematics, 113–28. Providence, Rhode Island: American Mathematical Society, 2000. http://dx.doi.org/10.1090/gsm/025/05.

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Conference papers on the topic "Twisted Dirac operators"

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Gattringer, 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.

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