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Journal articles on the topic 'Twisted Dirac operators'

Author: Grafiati

Published: 14 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Branding, Volker. "A note on twisted Dirac operators on closed surfaces." Differential Geometry and its Applications 60 (October 2018): 54–65. http://dx.doi.org/10.1016/j.difgeo.2018.05.006.

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12

Zhang, Dapeng. "Projective Dirac operators, twisted K-theory and local index formula." Journal of Noncommutative Geometry 8, no. 1 (2014): 179–215. http://dx.doi.org/10.4171/jncg/153.

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13

Miatello, Roberto J., and Ricardo A. Podestá. "The spectrum of twisted Dirac operators on compact flat manifolds." Transactions of the American Mathematical Society 358, no. 10 (May 9, 2006): 4569–603. http://dx.doi.org/10.1090/s0002-9947-06-03873-6.

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14

Almorox, Antonio López, and Carlos Tejero Prieto. "Holomorphic spectrum of twisted Dirac operators on compact Riemann surfaces." Journal of Geometry and Physics 56, no. 10 (October 2006): 2069–91. http://dx.doi.org/10.1016/j.geomphys.2005.11.007.

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15

Benameur, Moulay Tahar, and Varghese Mathai. "Conformal invariants of twisted Dirac operators and positive scalar curvature." Journal of Geometry and Physics 70 (August 2013): 39–47. http://dx.doi.org/10.1016/j.geomphys.2013.03.010.

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16

Paradan, Paul-Émile, and Michèle Vergne. "The multiplicities of the equivariant index of twisted Dirac operators." Comptes Rendus Mathematique 352, no. 9 (September 2014): 673–77. http://dx.doi.org/10.1016/j.crma.2014.05.001.

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17

Wang, Jian, and Yong Wang. "Twisted Dirac operators and the noncommutative residue for manifolds with boundary." Journal of Pseudo-Differential Operators and Applications 7, no. 2 (November 30, 2015): 181–211. http://dx.doi.org/10.1007/s11868-015-0139-3.

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18

LIM, YUHAN. "DEFINING AN SU(3)-CASSON/U(2)-SEIBERG–WITTEN INTEGER INVARIANT FOR INTEGRAL HOMOLOGY 3-SPHERES." Communications in Contemporary Mathematics 09, no. 03 (June 2007): 359–400. http://dx.doi.org/10.1142/s0219199707002447.

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An open question is the possibility of defining an integer valued SU(3)-Casson invariant for integral homology 3-spheres which involves counting the irreducible portion of the non-degenerate (perturbed) moduli space of flat SU(3)-connections plus counter-terms associated to only the non-degenerate (perturbed) reducible portion of the moduli space. The obstruction to this is the non-trivial spectral flow of a family of twisted signature operators in 3-dimensions. The parallel U(2)-Seiberg–Witten theory also has a similiar obstruction but arising from the non-trivial spectral flow of a family of twisted Dirac operators. By taking the SU(3)-flat and U(2)-Seiberg–Witten equations simultaneously the obstructions can be made to cancel and an integer invariant is obtained.

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19

Yu, Jianqing. "Higher spectral flow for Dirac operators with local boundary conditions." International Journal of Mathematics 27, no. 08 (July 2016): 1650068. http://dx.doi.org/10.1142/s0129167x16500683.

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We consider a one parameter family [Formula: see text] of families of fiberwise twisted Dirac type operators on a fibration with the typical fiber an even dimensional compact manifold with boundary, which verifies [Formula: see text] with [Formula: see text] being a smooth map from the fibration to a unitary group [Formula: see text]. For each [Formula: see text], we impose on [Formula: see text] a certain fixed local elliptic boundary condition [Formula: see text] and get a self-adjoint extension [Formula: see text]. Under the assumption that [Formula: see text] has vanishing [Formula: see text]-index bundle, we establish a formula for the higher spectral flow of [Formula: see text], [Formula: see text]. Our result generalizes a recent result of [A. Gorokhovsky and M. Lesch, On the spectral flow for Dirac operators with local boundary conditions, Int. Math. Res. Not. IMRN (2015) 8036–8051.] to the families case.

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20

Kac, Victor G., Pierluigi Möseneder Frajria, and Paolo Papi. "Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting." Advances in Mathematics 217, no. 6 (April 2008): 2485–562. http://dx.doi.org/10.1016/j.aim.2007.10.005.

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21

AZZALI, SARA, and CHARLOTTE WAHL. "Two-cocycle twists and Atiyah–Patodi–Singer index theory." Mathematical Proceedings of the Cambridge Philosophical Society 167, no. 3 (August 22, 2018): 437–87. http://dx.doi.org/10.1017/s0305004118000427.

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AbstractWe construct η- and ρ-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah–Patodi–Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.

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22

Tian, Youliang, and Weiping Zhang. "Symplectic reduction and a weighted multiplicity formula for twisted $\mathrm{Spin}^c$-Dirac operators." Asian Journal of Mathematics 2, no. 3 (1998): 591–608. http://dx.doi.org/10.4310/ajm.1998.v2.n3.a5.

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23

Cecchini, Simone. "Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds." Journal of Topology and Analysis 12, no. 04 (November 16, 2018): 897–939. http://dx.doi.org/10.1142/s1793525319500687.

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A Dirac-type operator on a complete Riemannian manifold is of Callias-type if its square is a Schrödinger-type operator with a potential uniformly positive outside of a compact set. We develop the theory of Callias-type operators twisted with Hilbert [Formula: see text]-module bundles and prove an index theorem for such operators. As an application, we derive an obstruction to the existence of complete Riemannian metrics of positive scalar curvature on noncompact spin manifolds in terms of closed submanifolds of codimension one. In particular, when [Formula: see text] is a closed spin manifold, we show that if the cylinder [Formula: see text] carries a complete metric of positive scalar curvature, then the (complex) Rosenberg index on [Formula: see text] must vanish.

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24

Hanisch, Florian, and Matthias Ludewig. "A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold." Communications in Mathematical Physics 391, no. 3 (February 21, 2022): 1209–39. http://dx.doi.org/10.1007/s00220-022-04336-7.

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AbstractWe give a rigorous construction of the path integral in $${\mathcal {N}}=1/2$$ N = 1 / 2 supersymmetry as an integral map for differential forms on the loop space of a compact spin manifold. It is defined on the space of differential forms which can be represented by extended iterated integrals in the sense of Chen and Getzler–Jones–Petrack. Via the iterated integral map, we compare our path integral to the non-commutative loop space Chern character of Güneysu and the second author. Our theory provides a rigorous background to various formal proofs of the Atiyah–Singer index theorem for twisted Dirac operators using supersymmetric path integrals, as investigated by Alvarez-Gaumé, Atiyah, Bismut and Witten.

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25

Benameur, Moulay Tahar, and Varghese Mathai. "Corrigendum to “Conformal invariants of twisted Dirac operators and positive scalar curvature” [J. Geom. Phys. 70 (2013) 39–47]." Journal of Geometry and Physics 76 (February 2014): 263–64. http://dx.doi.org/10.1016/j.geomphys.2013.11.003.

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26

Kac, Victor G., Pierluigi Möseneder Frajria, and Paolo Papi. "Corrigendum to “Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting” [Adv. Math. 217 (6) (2008) 2485–2562]." Advances in Mathematics 351 (July 2019): 1201–9. http://dx.doi.org/10.1016/j.aim.2019.04.061.

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27

IVANOV, E. A., and A. V. SMILGA. "DIRAC OPERATOR ON COMPLEX MANIFOLDS AND SUPERSYMMETRIC QUANTUM MECHANICS." International Journal of Modern Physics A 27, no. 25 (October 10, 2012): 1230024. http://dx.doi.org/10.1142/s0217751x12300244.

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We explore a simple [Formula: see text] supersymmetric quantum mechanics (SQM) model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum [Formula: see text] can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah–Singer theorem.

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28

Turtoi, Adriana. "Twisted dirac operator on minimal submanifolds." Rendiconti del Circolo Matematico di Palermo 55, no. 2 (June 2006): 192–202. http://dx.doi.org/10.1007/bf02874702.

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29

Jardim, Marcos, and Rafael F. Leão. "On the eigenvalues of the twisted Dirac operator." Journal of Mathematical Physics 50, no. 6 (June 2009): 063513. http://dx.doi.org/10.1063/1.3133944.

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30

Feng, Huitao, and Enli Guo. "A super-twisted Dirac operator and Novikov inequalities." Science in China Series A: Mathematics 43, no. 5 (May 2000): 470–80. http://dx.doi.org/10.1007/bf02897139.

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31

Fosco, C. D., and S. Randjbar-Daemi. "Determinant of twisted chiral Dirac operator on the lattice." Physics Letters B 354, no. 3-4 (July 1995): 383–88. http://dx.doi.org/10.1016/0370-2693(95)00599-g.

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32

IONESCU, ADRIAN MIHAI, VLADIMIR SLESAR, MIHAI VISINESCU, and GABRIEL EDUARD VÎLCU. "TRANSVERSAL KILLING AND TWISTOR SPINORS ASSOCIATED TO THE BASIC DIRAC OPERATORS." Reviews in Mathematical Physics 25, no. 08 (September 2013): 1330011. http://dx.doi.org/10.1142/s0129055x13300112.

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We study the interplay between the basic Dirac operator and the transversal Killing and twistor spinors. In order to obtain results for the general Riemannian foliations with bundle-like metric, we consider transversal Killing spinors that appear as natural extension of the harmonic spinors associated with the basic Dirac operator. In the case of foliations with basic-harmonic mean curvature, it turns out that this type of spinors coincide with the standard definition. We obtain the corresponding version of classical results on closed Riemannian manifold with spin structure, and extending some previous results.

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33

Tsai, Chung-Jun. "Asymptotic spectral flow for Dirac operators of disjoint Dehn twists." Asian Journal of Mathematics 18, no. 4 (2014): 633–86. http://dx.doi.org/10.4310/ajm.2014.v18.n4.a5.

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34

Habib, Georges, and Roger Nakad. "The twisted Spinc Dirac operator on Kähler submanifolds of the complex projective space." Journal of Geometry and Physics 77 (March 2014): 43–47. http://dx.doi.org/10.1016/j.geomphys.2013.12.003.

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35

Ginoux, Nicolas, and Georges Habib. "The spectrum of the twisted Dirac operator on Kähler submanifolds of the complex projective space." Manuscripta Mathematica 137, no. 1-2 (May 29, 2011): 215–31. http://dx.doi.org/10.1007/s00229-011-0467-4.

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36

Galina, Esther, and Jorge Vargas. "Eigenvalues and Eigenspaces for the Twisted Dirac Operator over SU(N, 1) and Spin(2N, 1)." Transactions of the American Mathematical Society 345, no. 1 (September 1994): 97. http://dx.doi.org/10.2307/2154597.

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37

Albanese, Michael, and Aleksandar Milivojević. "Connected sums of almost complex manifolds, products of rational homology spheres, and the twisted spin Dirac operator." Topology and its Applications 267 (November 2019): 106890. http://dx.doi.org/10.1016/j.topol.2019.106890.

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38

Galina, Esther, and Jorge Vargas. "Eigenvalues and eigenspaces for the twisted Dirac operator over ${\rm SU}(N,1)$ and ${\rm Spin}(2N,1)$." Transactions of the American Mathematical Society 345, no. 1 (January 1, 1994): 97–113. http://dx.doi.org/10.1090/s0002-9947-1994-1189792-6.

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39

Brzeziński, Tomasz, Nicola Ciccoli, Ludwik Dąbrowski, and Andrzej Sitarz. "Twisted Reality Condition for Dirac Operators." Mathematical Physics, Analysis and Geometry 19, no. 3 (July 18, 2016). http://dx.doi.org/10.1007/s11040-016-9219-8.

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40

Tarviji, Arezo, and Morteza Mirmohammad Rezaei. "DIRAC OPERATORS ON LIE ALGEBROIDS." Facta Universitatis, Series: Mathematics and Informatics, February 2, 2021, 983. http://dx.doi.org/10.22190/fumi2004983t.

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We compare the Dirac operator on transitive Riemannian Lie algebroid equipped by spin or complex spin structure with the one defined on to its base manifold‎. Consequently we derive upper eigenvalue bounds of Dirac operator on base manifold of spin Lie algebroid twisted with the spinor bundle of kernel bundle‎.

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41

EKER, Serhan. "Estimation on The Spinc Twisted Dirac Operators." Hacettepe Journal of Mathematics and Statistics, December 31, 2022, 1–9. http://dx.doi.org/10.15672/hujms.1054157.

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42

Freidel, Laurent, Marc Geiller, and Daniele Pranzetti. "Edge modes of gravity. Part III. Corner simplicity constraints." Journal of High Energy Physics 2021, no. 1 (January 2021). http://dx.doi.org/10.1007/jhep01(2021)100.

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Abstract In the tetrad formulation of gravity, the so-called simplicity constraints play a central role. They appear in the Hamiltonian analysis of the theory, and in the Lagrangian path integral when constructing the gravity partition function from topological BF theory. We develop here a systematic analysis of the corner symplectic structure encoding the symmetry algebra of gravity, and perform a thorough analysis of the simplicity constraints. Starting from a precursor phase space with Poincaré and Heisenberg symmetry, we obtain the corner phase space of BF theory by imposing kinematical constraints. This amounts to fixing the Heisenberg frame with a choice of position and spin operators. The simplicity constraints then further reduce the Poincaré symmetry of the BF phase space to a Lorentz subalgebra. This picture provides a particle-like description of (quantum) geometry: the internal normal plays the role of the four-momentum, the Barbero-Immirzi parameter that of the mass, the flux that of a relativistic position, and the frame that of a spin harmonic oscillator. Moreover, we show that the corner area element corresponds to the Poincaré spin Casimir. We achieve this central result by properly splitting, in the continuum, the corner simplicity constraints into first and second class parts. We construct the complete set of Dirac observables, which includes the generators of the local $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{C}}\right) $$ sl 2 ℂ subalgebra of Poincaré, and the components of the tangential corner metric satisfying an $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{R}}\right) $$ sl 2 ℝ algebra. We then present a preliminary analysis of the covariant and continuous irreducible representations of the infinite-dimensional corner algebra. Moreover, as an alternative path to quantization, we also introduce a regularization of the corner algebra and interpret this discrete setting in terms of an extended notion of twisted geometries.

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43

Cichy, Krzysztof, Elena Garcia-Ramos, and Karl Jansen. "Chiral condensate from the twisted mass Dirac operator spectrum." Journal of High Energy Physics 2013, no. 10 (October 2013). http://dx.doi.org/10.1007/jhep10(2013)175.

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44

Cichy, Krzysztof, Elena Garcia-Ramos, and Karl Jansen. "Topological susceptibility from the twisted mass Dirac operator spectrum." Journal of High Energy Physics 2014, no. 2 (February 2014). http://dx.doi.org/10.1007/jhep02(2014)119.

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45

Liu, Siyao, and Yong Wang. "A Kastler–Kalau–Walze Type Theorem for the J-Twist $$D_{J}$$ of the Dirac Operator." Journal of Nonlinear Mathematical Physics, January 20, 2023. http://dx.doi.org/10.1007/s44198-022-00100-6.

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AbstractIn this paper, we give a Lichnerowicz type formula for the J-twist $$D_{J}$$ D J of the Dirac operator. And we prove a Kastler–Kalau–Walze type theorem for the J-twist $$D_{J}$$ D J of the Dirac operator on three-dimensional and four-dimensional almost product Riemannian spin manifold with boundary.

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46

DLAMINI, A., EMILE F. DOUNGMO GOUFO, and M. KHUMALO. "CHAOTIC BEHAVIOR OF MODIFIED STRETCH–TWIST–FOLD FLOW UNDER FRACTAL-FRACTIONAL DERIVATIVES." Fractals, September 24, 2022. http://dx.doi.org/10.1142/s0218348x22402071.

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The application of the recently proposed integral and differential operators known as the fractal-fractional derivatives and integrals has opened doors to ongoing research in different fields of science, engineering, and technology. These operators are a convolution of the fractal derivative with the generalized Mittag-Leffler function with Delta-Dirac property, the power law, and the exponential decay law with Delta-Dirac property. In this paper, we aim to extend the work in the literature by applying these operators to a modified stretch–twist–fold (STF) flow based on the STF flow related to the motion of particles in fluids that naturally occur in the dynamo theorem. We want to capture the dynamical behavior of the modified STF flow under these operators. We will present the numerical schemes that can be used to solve these nonlinear systems of differential equations. We will also consider numerical simulations for different values of fractional order and fractal dimension.

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47

Schmüdgen, K., and E. Wagner. "Dirac operator and a twisted cyclic cocycle on the standard Podles quantum sphere." Journal für die reine und angewandte Mathematik (Crelles Journal) 2004, no. 574 (January 4, 2004). http://dx.doi.org/10.1515/crll.2004.072.

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48

Cichy, Krzysztof. "Quark mass anomalous dimension and Λ MS ¯ $$ {\varLambda}_{\overline{\mathrm{MS}}} $$ from the twisted mass Dirac operator spectrum." Journal of High Energy Physics 2014, no. 8 (August 2014). http://dx.doi.org/10.1007/jhep08(2014)127.

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49

Takayanagi, Tadashi, and Takashi Tsuda. "Free fermion cyclic/symmetric orbifold CFTs and entanglement entropy." Journal of High Energy Physics 2022, no. 12 (December 1, 2022). http://dx.doi.org/10.1007/jhep12(2022)004.

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Abstract In this paper we study the properties of two-dimensional CFTs defined by cyclic and symmetric orbifolds of free Dirac fermions, especially by focusing on the partition function and entanglement entropy. Via the bosonization, we construct the twist operators which glue two complex planes to calculate the partition function of ℤ2 orbifold CFT on a torus. We also find an expression of ℤN cyclic orbifold in terms of Hecke operators, which provides an explicit relation between the partition functions of cyclic orbifolds and those of symmetric ones. We compute the entanglement entropy and Renyi entropy in cyclic orbifolds on a circle both for finite temperature states and for time-dependent states under quantum quenches. We find that the replica method calculation is highly non-trivial and new because of the contributions from replicas with different boundary conditions. We find the full expression for the ℤ2 orbifold and show that the periodicity gets doubled. Finally, we discuss extensions of our results on entanglement entropy to symmetric orbifold CFTs and make a heuristic argument towards holographic CFTs.

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