In line with a previous paper, a gauge-invariant regularization is developed for the Weyl determinant of a Euclidean gauged chiral fermion. We restrict ourselves to gauge configurations with the A field going to zero at infinity in Euclidean space; and thus restrict gauge transformations to those with U the identity at infinity. For each finite cutoff one gets a strictly gauge-invariant express...

We are concern about a conjecture proposed in the middle of the seventies by Hellesseth in the framework of maximal sequences and theirs crosscorrelations. The conjecture claims the existence of a zero outphase Fourier coefficient. We give some divisibility properties in this direction. 1. Two conjectures of Helleseth Let L be a finite field of order q > 2 and characteristic p. Let μ be the can...

Lyapunov exponents of a dynamical system are a useful tool to gauge the stability and complexity of the system. This paper offers a definition of Lyapunov exponents for a sequence of free linear operators. The definition is based on the concept of the extended Fuglede-Kadison determinant. We establish the existence of Lyapunov exponents, derive formulas for their calculation, and show that Lyap...

A global anomaly in a chiral gauge theory manifests itself in different ways in the continuum and on the lattice. In the continuum case, functional integration of the fermion determinant over the whole space of gauge fields yields zero. In the case of the lattice, it is not even possible to define a fermion measure over the whole space of gauge configurations. However, this is not necessary, an...

The focal points of a curve traced by a planar linkage capture essential information about the curve. In a previous paper, we showed how to determine the singular foci of planar linkages from an expression for the tracing curve derived by use of the Dixon determinant. This paper gives an alternative approach to finding the singular foci, one that lends itself to simple geometric interpretations...

We present two improvements to our previous dynamical overlap HMC algorithm. We introduce a new method of differentiating the eigenvectors of the Kernel operator, which removes an instability in the fermionic force. Secondly, by simulating part of the fermion determinant exactly, without pseudo-fermions, we are able to increase the rate of topological tunnelling by a factor of more than ten, re...

In this paper, we present a method for the computation of the low-lying real eigenvalues of the Wilson-Dirac operator based on the Arnoldi algorithm. These eigenvalues contain information about several observables. We used them to calculate the sign of the fermion determinant in oneflavor QCD and the sign of the Pfaffian in N = 1 super Yang-Mills theory. The method is based on polynomial transf...

Flagged Schur functions are generalizations of Schur functions. They appear in the work of Lascoux and Schutzenberger [2] in their study of Schubert polynomials. Gessel [ 1 ] has shown that flagged Schur functions can be expressed both as a determinant in the complete homogeneous symmetric functions and in terms of column-strict tableaux just as can ordinary Schur functions (Jacobi-Trudi identi...

The microscopic approach for studying the half-filled state of the fractional quantum Hall effect is based on the idea of proposing a trial Fermi wave function of the Jastrow-Slater form, which is then fully projected onto the lowest Landau level. A simplified starting point is to drop the projection operator and to consider an unprojected wave function. A recent study claims that such a wave f...

Exceptional orthogonal polynomials were introduced by Gomez-Ullate, Kamran and Milson as polynomial eigenfunctions of second order differential equations with the remarkable property that some degrees are missing, i.e., there is not a polynomial for every degree. However, they do constitute a complete orthogonal system with respect to a weight function that is typically a rational modification ...