Related papers: On a Casher-Banks relation in MQCD

We derive exact analytical expressions for the spectral density of the Dirac operator at fixed \theta-angle in the microscopic domain of one-flavor QCD. These results are obtained by performing the sum over topological sectors using novel…

The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated. We use the analytical result for the eigenvalue density in the microscopic regime which…

QCD monopoles are magnetically charged quasiparticles whose Bose-Einstein condensation (BEC) at $T<T_c$ creates electric confinement and flux tubes. The "magnetic scenario" of QCD proposes that scattering on the non-condensed component of…

We give a formula for the first eigenvalue of the Dirac operator acting on spinor fields of a spin compact irreducible symmetric space $G/K$.

We report on the behavior of the eigenvalue distribution of the Dirac operator in (2+1)-flavor QCD at finite temperature, using the HISQ action. We calculate the eigenvalue density at several values of the temperature close to the…

We consider the eigenvalue problem of a kinetic collision operator for a quantum Brownian particle interacting with a one-dimensional chain. The quantum nature of the system gives rise to a difference operator. For the one-dimensional case,…

Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields…

We consider the 3-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated in the upper…

The Dirac operator is considered on a bidimensional domain whose boundary carries the infinite mass boundary condition. The analysis is focused on the existence of discrete spectrum and on its asymptotic description in the thin width limit.…

The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-self-adjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that…

We study the behavior of the spectrum of the Dirac operator on collapsing S^1-bundles. Convergent eigenvalues will exist if and only if the spin structure is projectable.

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of…

Assume that the compact Riemannian spin manifold $(M^n,g)$ admits a $G$-structure with characteristic connection $\nabla$ and parallel characteristic torsion ($\nabla T=0$), and consider the Dirac operator $D^{1/3}$ corresponding to the…

We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…

We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the…

We discuss the covariant formulation of local field theories described by the Companion Lagrangian associated with p-branes. The covariantisation is shown to be useful for clarifying the geometrical meaning of the field equations and also…

This introductory presentation describes the Overlap Dirac Operator, why it could be useful in numerical QCD, and how it can be implemented.

We compute the low-lying spectrum of the staggered Dirac operator above and below the finite temperature phase transition in both quenched QCD and in dynamical four flavor QCD. In both cases we find, in the high temperature phase, a density…

In this lecture we discuss correlations of the QCD Dirac eigenvalues. We find that below a scale of $E_c\sim \Lambda/L^2$ they are given by chiral Random Matrix Theory. This follows from analytical arguments based on partially quenched…

We consider the Schrodinger operator with a constant magnetic field in the exterior of a compact domain on the plane. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We discuss the rate of…