相关论文: Fun with Dirac eigenvalues
Starting from thermalized quenched SU(2) configurations we apply cooling or iterated smearing, respectively, to produce sequences of gauge configurations with less and less fluctuations. We compute the low lying spectrum and eigenmodes of…
The one particle sector of the simplest one dimensional quantum lattice gas automaton has been observed to simulate both the (relativistic) Dirac and (nonrelativistic) Schroedinger equations, in different continuum limits. By analyzing the…
In the low energy effective theory describing the partially quenched extension of two light Wilson fermions, three low energy constants (LECs) appear in terms proportional to a^2 (a being the lattice spacing). We propose methods to…
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…
Recent developments and selected topics in low-energy QCD are summarized, from chiral effective field theory to systems with strange and charm quarks, from lattice QCD to precision experiments.
Discrete versions of the Laplace and Dirac operators haven been studied in the context of combinatorial models of statistical mechanics and quantum field theory. In this paper we introduce several variations of the Laplace and Dirac…
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…
In two previous papers, we started a study of the first eigenvalue of the Dirac operator on compact spin symmetric spaces, providing, for symmetric spaces of "inner" type, a formula giving this first eigenvalue in terms of the algebraic…
The lattice formulation of gauge theories in a renormalizable gauge is discussed. The formulation invokes a new phase diagram, and it may allow for a lattice definition of Chiral Gauge Theories.
We consider the Dirac equation with a generalized uncertainty principle in the presence of the Harmonic interaction and an external magnetic field. By doing the study in the momentum space, the problem solved in an exact analytical manner…
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary…
The statistical properties of the spectrum of the staggered Dirac operator in an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and at the spectrum edge. Two commonly used statistics, the number variance and the…
Long-wave low-frequency oscillations are described in a Wigner crystal by generalization of the reverse continuum model for the case of electronic lattice. The internal self-consistent long-wave electromagnetic field is used to describe the…
For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from…
I give an elementary introduction to the study of gauge theories coupled to fermions with many degrees of freedom. Besides their intrinsic interest, these theories are candidates for nonperturbative extensions of the Higgs sector of the…
The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in…
Lattice gauge theory is our primary tool for the study of non-perturbative phenomena in hadronic physics. In addition to giving quantitative information on confinement, the approach is yielding first principles calculations of hadronic…
I define lattice fermions in five Euclidean dimensions and the corresponding effective theory in four dimensions. The main properties of these theories include the suppression of high momentum modes of the lattice Dirac operator and their…
We give a min-max characterization of the weighted Dirac eigenvalues, and show that the weighted eigenvalues and eigenspaces of Dirac operators are continuous with respect to weak $L^p$ convergence of the inverse weight, for any $p>n$.…
For a long time, investigation into the weak interactions of quarks has guided us toward understanding the Standard Model we know today. Now in the era of high precision, these studies are still one of the most promising avenues for peering…