Related papers: Dirac operator normality and chiral properties

In this paper, we consider a discontinuous Dirac operator depending polynomially on the spectral parameter and a finite number of transmission conditions. We get some properties of eigenvalues and eigenfunctions. Then, we investigate some…

We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the…

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…

The family of Tremblay-Turbiner-Winternitz (TTW) Hamiltonians $H_k$ on a plane, corresponding to any positive real value of $k$, is shown to admit another ${\cal N} = 2$ supersymmetric extension than that previously introduced by the…

We obtain the Ward identities and the gauge-dependence of Green's functions in non-Abelian gauge theories by using only the canonical commutation relations and the equations of motion for the Heisenberg operators. The consideration is…

I discuss the consequences of the constraints imposed on the Dirac spectrum by the restoration of chiral symmetry in the chiral limit of gauge theories with two light fermion flavors, with particular attention to the fate of the anomalous…

The half-line Dirac operators with $L^2$-potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the…

We present a chiral solution of the Ginsparg-Wilson equation. This work is motivated by our recent proposal for nonperturbatively regulating chiral gauge theories, where five-dimensional domain wall fermions couple to a four-dimensional…

We introduce a lattice symmetry relation for field theories with general linear symmetries. For chiral symmetry the well-known Ginsparg-Wilson relation is reproduced. The new relation encodes the remnant of the original symmetry on the…

Let $\Omega_+\subset\mathbb{R}^{3}$ be a fixed bounded domain with boundary $\Sigma = \partial\Omega_{+}$. We consider $\mathcal{U}^\varepsilon$ a tubular neighborhood of the surface $\Sigma$ with a thickness parameter $\varepsilon>0$, and…

We find all spin operators for a Dirac particle satisfying the following very general conditions: (i) spin does not convert positive (negative) energy states into negative (positive) energy states, (ii) spin is a pseudo-vector, and (iii)…

We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained.

The importance of the spectral density of the Dirac operator in studying spontaneous chiral symmetry breaking and anomalous U(1) axial symmetry breaking are reviewed. It is shown that both types of symmetry breaking can be traced to effects…

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and…

We introduce Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories. We show that they are equivalent to the $\epsilon$-limit of the chiral Lagrangian for Wilson chiral perturbation theory. Results are obtained…

At nonzero density the eigenvalues of the Dirac operator move into the complex plane, while its singular values remain real and nonnegative. In QCD-like theories, the singular-value spectrum carries information on the diquark (or pionic)…

In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are provided, which are generalizations of the well-known Weyl…

We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via…

We reinvestigate constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature, employing the overlap Dirac operator with the exact chiral symmetry at finite lattice spacings…

We develop a theory of regularity for Dirac operators with uniformly locally square-integrable operator data. This is motivated by Stahl--Totik regularity for orthogonal polynomials and by recent developments for continuum Schr\"odinger…