Spin Structure and Dirac Operator

2013 ◽  
pp. 148-177
Author(s):  
Amiya Mukherjee
Keyword(s):  
Dirac Operator ◽  
Spin Structure

scholarly journals Adiabatic limit of the eta invariant over cofinite quotients of PSL(2, ℝ)

2008 ◽  
Vol 144 (6) ◽  
pp. 1593-1616 ◽  
Author(s):  
Paul Loya ◽  
Sergiu Moroianu ◽  
Jinsung Park
Keyword(s):  
Riemann Surface ◽  
Dirac Operator ◽  
Continuous Spectrum ◽  
Spin Structure ◽  
Adiabatic Limit ◽  
Regularized Trace ◽  
Standard Definition ◽  
Eta Invariant ◽  
Hyperbolic Riemann Surface

AbstractThe eta invariant of the Dirac operator over a non-compact cofinite quotient of PSL(2,ℝ) is defined through a regularized trace following Melrose. It reduces to the standard definition in terms of eigenvalues in the case of a totally non-trivial spin structure. When the S1-fibers are rescaled, the metric becomes of non-exact fibered-cusp type near the ends. We completely describe the continuous spectrum of the Dirac operator with respect to the rescaled metric and its dependence on the spin structure, and show that the adiabatic limit of the eta invariant is essentially the volume of the base hyperbolic Riemann surface with cusps, extending some of the results of Seade and Steer.

scholarly journals DIRAC OPERATORS ON LIE ALGEBROIDS

2021 ◽  
pp. 983
Author(s):  
Arezo Tarviji ◽  
Morteza Mirmohammad Rezaei
Keyword(s):  
Dirac Operator ◽  
Spin Structure ◽  
Dirac Operators ◽  
Lie Algebroids ◽  
Lie Algebroid ◽  
Eigenvalue Bounds ◽  
Base Manifold ◽  
Spinor Bundle ◽  
Complex Spin ◽  
The One

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.

scholarly journals Twistor spaces and the adiabatic limits of Dirac operators

2001 ◽  
Vol 164 ◽  
pp. 53-73 ◽  
Author(s):  
Masayoshi Nagase
Keyword(s):  
Dirac Operator ◽  
Spin Structure ◽  
Twistor Space ◽  
Dirac Operators ◽  
Twistor Spaces ◽  
Adiabatic Limits ◽  
Twisted Dirac Operator

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.

scholarly journals TRANSVERSAL KILLING AND TWISTOR SPINORS ASSOCIATED TO THE BASIC DIRAC OPERATORS

2013 ◽  
Vol 25 (08) ◽  
pp. 1330011 ◽  
Author(s):  
ADRIAN MIHAI IONESCU ◽  
VLADIMIR SLESAR ◽  
MIHAI VISINESCU ◽  
GABRIEL EDUARD VÎLCU
Keyword(s):  
Riemannian Manifold ◽  
Dirac Operator ◽  
Mean Curvature ◽  
Spin Structure ◽  
Natural Extension ◽  
Dirac Operators ◽  
Harmonic Mean ◽  
Standard Definition ◽  
Killing Spinors ◽  
Harmonic Spinors

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.

Interaction of ditertiary phosphines with phenyl- and 1-naphthyldithiocarbamatonickel(II)

1985 ◽  
Vol 50 (6) ◽  
pp. 1383-1390
Author(s):  
Aref A. M. Aly ◽  
Ahmed A. Mohamed ◽  
Mahmoud A. Mousa ◽  
Mohamed El-Shabasy
Keyword(s):  
Thermal Analysis ◽  
Powder Diffraction ◽  
Spin Structure ◽  
Magnetic Measurements ◽  
Mixed Ligand ◽  
Mixed Ligand Complexes ◽  
X Ray ◽  
Square Planar

The synthesis of the following mixed ligand complexes is reported: [Ni(phdtc)2(dpm)2], [Ni(phdtc)2(dpe)2], [Ni(phdtc)2(dpp)3], [Ni(1-naphdtc)2(dpm)2], [Ni(1-naphdtc)2], and [Ni(1-naphdtc)2(dpp)2], where phdtc = PhNHCSS-, 1-naphdtc = 1-NaPhNHCSS-, dpm = Ph2PCH2PPh2, dpe = Ph2P(CH2)2PPh2, and dpp = Ph2P(CH2)3PPh2. The complexes are characterised by microanalysis, IR and UV-Vis spectra, magnetic measurements, conductivity, X-ray powder diffraction, and thermal analysis. All the mixed ligand complexes are diamagnetic, and thus a square-planar or square-pyramidal (low-spin) structure was proposed for the present complexes.

scholarly journals Extended supersymmetries and the Dirac operator

2005 ◽  
Vol 315 (2) ◽  
pp. 467-487 ◽  
Author(s):  
A. Kirchberg ◽  
J.D. Länge ◽  
A. Wipf
Keyword(s):  
Dirac Operator

Corrigendum to “Spin structure relation to phase contrast imaging of isolated magnetic Bloch and Néel skyrmions” [Ultramicroscopy 212 (2020) 112973]

2021 ◽  
Vol 223 ◽  
pp. 113224
Author(s):  
S. Pöllath ◽  
T. Lin ◽  
N. Lei ◽  
W. Zhao ◽  
J. Zweck ◽  
...  
Keyword(s):  
Phase Contrast ◽  
Spin Structure ◽  
Phase Contrast Imaging ◽  
Contrast Imaging ◽  
Structure Relation
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