In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions in the fundamental representation of SU(N) gauge group in the background of an instanton with non-trivial holonomy at spatial infinity. This object, called the Kraan–van Baal – Lee–Lu caloron, can be viewed as composed of N Bogomolny–Prasad–Sommerfeld monopoles (or dyons). We compute analytically tw...

Research supported by the Natural Sciences and Engineering Research Council (Canada) and Fonds pour la Formation de Chercheurs et l'Aide a la Recherche (Quebec). Some results in section 3 of this work are taken from Jha's Ph.D. thesis [Jha 1992]. After a brief review of partial results regarding Case I of Fermat’s Last Theorem, we discuss the relationship between the number of points on Fermat’...

In the paper, the authors find a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.

We show how the prescription of taking the absolute value of the fermion determinant in the integration measure of QCD at finite density, forgetting its phase, reproduces the correct thermodynamical limit. This prescription, which applies also to other gauge theories with non-positive-definite integration measure, also has the advantage of killing finite size effects due to extremely small mean...

The purpose of this note is to define a tri-moment map for certain manifolds with an Sp(1)-action. We show how this map can be used ro reduce such manifolds. The images of such maps for quaternionic flag manifolds, which are defined using the Dieudonné determinant, resemble the polytopes from the complex case.

A method is presented for using truncated, maximally localized Wannier functions to introduce sparsity into the Slater determinant part of the trial wave function in quantum Monte Carlo calculations. When combined with an efficient numerical evaluation of these localized orbitals, the dominant cost in the calculation, namely, the evaluation of the Slater determinant, scales linearly with system...

Recently, a beautiful identity due to Borodin and Okounkov was proved for Toeplitz determinants which shows how one can write a Toeplitz determinant as a Fredholm determinant. In this note we generalize this to the Wiener-Hopf case. The proof in the Wiener-Hopf case follows identically with the second one given in [1]. We include it here for completeness sake and because the nature of the ident...

We obtain a flagged form of the Cauchy determinant and establish a correspondence between this determinant and nonintersecting lattice paths, from which it follows that Cauchy identity on Schur functions. By choosing different origins and destinations for the lattice paths, we are led to an identity of Gessel on the Cauchy sum of Schur functions in terms of the complete symmetric functions in t...

There is a large body of literature on the problem of stability for inviscid shock waves and in particular for gas dynamics, see [2, 17, 3, 5, 6, 9, 10, 16, 4, 7, 21, 12, 13, 1, 14, 15, 24]. The purpose of this appendix is to calculate the Lopatinski determinant, or “stability function,” for the Euler equations of compressible gas dynamics. We describe two approaches to this problem. In the fir...