Related papers: Random matrix theory and spectral sum rules for th…
In this lecture we argue that the fluctuations of Dirac eigenvalues on the finest scale, i.e. on the scale of the average level spacing do not depend on the underlying dynamics and can be obtained from a chiral random matrix theory with the…
We extend QCD sum rule analysis to moderate energy fixed angle Compton scattering. In this kinematic region there is a strong similarity to the sum rule treatment of electromagnetic form factors, although the four-point amplitude requires a…
The chiral condensate in QCD at zero temperature does not depend on the quark chemical potential (up to one third the nucleon mass), whereas the spectral density of the Dirac operator shows a strong dependence on the chemical potential. The…
We derive the universality principle for empirical spectral distributions of sample covariance matrices and their Stieltjes transforms. This principle states the following. Suppose quadratic forms of random vectors $y_p$ in $R^p$ satisfy a…
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the…
We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma_5-hermitian, but its nonreal eigenvalues still…
Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial-vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special…
We compare eigenvalue correlations of the Dirac operator with a chemical potential obtained from lattice simulations of quenched QCD with analytic predictions obtained from chiral effective theories in the zero-momentum limit. By comparing…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
We derive QCD sum rules from the nucleon two-point function in nuclear medium, calculating its specral function in chiral perturbation theory to one loop. Our calculation shows the inadequacy of the commonly used ansatz to represent the…
I propose a controlled approximation to QCD-like theories with massless quarks by employing supersymmetric QCD perturbed by anomaly-mediated supersymmetry breaking. They have identical massless particle contents. Thanks to the…
In a four-dimensional quantum field theory that flows between two fixed points under the renormalization group, the change in the conformal anomaly $\Delta a$ has been related to the average null energy. We extend this result to derive a…
In connection with recent publications we discuss spectral sum rules for the Tomonaga-Luttinger model without using the explicit result for the one-electron Green's function. They are usefull in the interpretation of recent high resolution…
We compare the eigenvalue spectra of the Dirac operator from a simulation with two mass degenerate dynamical chirally improved fermions with Random Matrix Theory. Comparisons with distribution of k-th eigenvalues (k=1,2) in fixed…
Weak-coupling conserving approximations can be constructed by truncations of the Luttinger-Ward functional and are well known as thermodynamically consistent approaches which respect macroscopic conservation laws as well as certain sum…
We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate…
We shortly review some applications of the (inverse) Laplace (LSR) transform sum rules in Quantum ChromoDynamics (QCD) for extracting the fundamental QCD parameters (coupling constant $\alpha_s$, quark and gluon condensates) and the hadron…
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…
Normality and $\ga$-hermiticity are what gives rise to chiral properties and rules. The Ginsparg-Wilson (GW) relation is only one of the possible spectral constraints. The sum rule for chiral differences of real modes has important…
The Dirac operator enters into zero curvature representation for the cubic nonlinear Schr\"{o}dinger equation. We introduce and study a conformal map from the upper half-plane of the spectral parameter of the Dirac operator into itself. The…