Related papers: The k-th Smallest Dirac Operator Eigenvalue and th…
We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory…
According to the Banks-Casher formula the chiral order parameter is directly related to the spectrum of the Dirac operator. In this lecture, we will argue that some properties of the Dirac spectrum are universal and can be obtained from a…
We study the eigenvalue problem for a one-dimensional Dirac operator with a spatially varying ``mass'' term. It is well-known that when the mass function has the form of a kink, or \emph{domain wall}, transitioning between strictly positive…
Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model…
We present the ingredients necessary for the determination of physical K->pi pi decay amplitudes for Delta I=3/2 transitions, from lattice simulations at unphysical kinematics and the use of chiral perturbation theory at next-to-leading…
Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac operator in a well-defined finite-volume scaling regime.
The relativistic amplitudes of pion photoproduction are evaluated by dispersion relations at t=const. The imaginary parts of the amplitudes are taken from the MAID model covering the absorption spectrum up to center-of-mass energies W = 2.2…
The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy $E_c\propto 1/\sqrt{V}$, where $V$ is the physical volume. For somewhat larger…
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 prove that QCD in the epsilon-regime of chiral Perturbation Theory is equivalent to chiral Random Matrix Theory for zero and both non-zero real and imaginary chemical potential mu. To this aim we prove a theorem that relates integrals…
We calculate the spectral density of the Dirac operator over an ensemble of configurations composed of overlapping instantons and anti-instantons. We find evidence that the spectral density diverges in the limit of small eigenvalues. This…
We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action…
The gauge-invariant, nonlocal, dynamical quark model is proved to generate the minimal vertices which satisfy the Ward-Takahashi identities. In the chiral limit, the momentum-dependent quark self-energy results in a flat-like form with some…
We have calculated complete spectra of the staggered Dirac operator on the lattice in quenched SU(3) gauge theory for \beta = 5.4 and various lattice sizes. The microscopic spectral density, the distribution of the smallest eigenvalue, and…
For first order systems, we obtain an efficient bound on the exponential decay of an eigenfunction in terms of the distance between the corresponding eigenvalue and the essential spectrum. As an example, the Dirac operator is considered.
We use chiral perturbation theory to evaluate the scattering amplitude for the process Pi^+ K^- to Pi^+ K^- at leading and next-to-leading orders in the chiral counting and in the presence of isospin breaking effects. We also discuss the…
The pattern of chiral symmetry breaking is exploited to compute vector and axial-vector pion matrix elements in a uniform magnetic field. Our results are model independent, and thereby constitute low-energy theorems that must be obeyed by…
The three-particle $K$-matrix, $\mathcal{K}_{\mathrm{df},3}$, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we…
Quenched chiral perturbation theory is used to compute the first finite volume correction to the chiral condensate. The correction diverges logarithmically with the four-volume $V$. We point out that with dynamical quarks one can obtain…
We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions…