scholarly journals Perturbation calculation of the axial anomaly of a Ginsparg-Wilson lattice Dirac operator

2002 ◽  
Vol 65 (5) ◽  
Author(s):  
Ting-Wai Chiu ◽  
Tung-Han Hsieh
Keyword(s):  
Dirac Operator ◽  
Perturbation Calculation ◽  
Axial Anomaly

scholarly journals Axial anomaly with the overlap-Dirac operator in arbitrary dimensions

2002 ◽  
Vol 2002 (09) ◽  
pp. 025-025 ◽  
Author(s):  
Takanori Fujiwara ◽  
Keiichi Nagao ◽  
Hiroshi Suzuki
Keyword(s):  
Dirac Operator ◽  
Axial Anomaly ◽  
Arbitrary Dimensions

scholarly journals ON INDICES OF THE DIRAC OPERATOR IN A NON-FREDHOLM CASE

1996 ◽  
Vol 11 (12) ◽  
pp. 979-986
Author(s):  
ALEXANDER MOROZ
Keyword(s):  
Dirac Operator ◽  
Heat Kernel ◽  
Continuous Spectrum ◽  
Fredholm Operator ◽  
Axial Anomaly ◽  
Bohm Potential ◽  
Spectral Asymmetry ◽  
Aharonov Bohm ◽  
Dirac Hamiltonian

The Dirac–Hamiltonian with the Aharonov–Bohm potential provides an example of a non-Fredholm operator for which all spectral asymmetry comes entirely from the continuous spectrum. In this case one finds that the use of standard definitions of the resolvent regularized, the heat kernel regularized, and the Witten indices misses the contribution coming from the continuous spectrum and gives vanishing spectral asymmetry and axial anomaly. This behavior in the case of the continuous spectrum seems to be general and its origin is discussed.

scholarly journals Chiral waves on the Fermi-Dirac sea: Quantum superfluidity and the axial anomaly

2021 ◽  
Vol 966 ◽  
pp. 115385
Author(s):  
Emil Mottola ◽  
Andrey V. Sadofyev
Keyword(s):  
Axial Anomaly ◽  
Dirac Sea

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

scholarly journals Eigenvalue bounds for non-selfadjoint Dirac operators

2021 ◽  
Author(s):  
Piero D’Ancona ◽  
Luca Fanelli ◽  
Nico Michele Schiavone
Keyword(s):  
Dirac Operator ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Dirac Operators ◽  
Resolvent Estimates ◽  
Eigenvalue Bounds ◽  
Mixed Norms ◽  
Massless Case ◽  
Abstract Version ◽  
Embedded Eigenvalues

AbstractWe prove that the eigenvalues of the n-dimensional massive Dirac operator $${\mathscr {D}}_0 + V$$ D 0 + V , $$n\ge 2$$ n ≥ 2 , perturbed by a potential V, possibly non-Hermitian, are contained in the union of two disjoint disks of the complex plane, provided V is sufficiently small with respect to the mixed norms $$L^1_{x_j} L^\infty _{{\widehat{x}}_j}$$ L x j 1 L x ^ j ∞ , for $$j\in \{1,\dots ,n\}$$ j ∈ { 1 , ⋯ , n } . In the massless case, we prove instead that the discrete spectrum is empty under the same smallness assumption on V, and in particular the spectrum coincides with the spectrum of the unperturbed operator: $$\sigma ({\mathscr {D}}_0+V)=\sigma ({\mathscr {D}}_0)={\mathbb {R}}$$ σ ( D 0 + V ) = σ ( D 0 ) = R . The main tools used are an abstract version of the Birman–Schwinger principle, which allows in particular to control embedded eigenvalues, and suitable resolvent estimates for the Schrödinger operator.

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