Related papers: Fermionic determinant for dyons and instantons wit…
We demonstrate the existence of a broad class of non-perturbative fermionic solutions to the Euclidean supergravity equations of motion, which are half-BPS and nonsingular, possess zero action, and obey an (anti)self-duality condition.…
We consider a function $U=e^{-f_0}\prod_j^N f_j^{\alpha_j}$ on a real affine space, here $f_0,..,f_N$ are linear functions, $\alpha_1, ...,\alpha_N$ complex numbers. The zeros of the functions $f_1, ..., f_N$ form an arrangement of…
The article describes a purely topological counterpart of the $\epsilon$-factorization of constants in the functional equations (which is a key ingredient in the interplay between L-functions and classical automorphic forms). We consider…
From spinor and scalar 2+1 dimensional QED effective actions at finite temperature and density in a constant magnetic field background, we calculate the corresponding virial coefficients for particles in the lowest Landau level. These…
The statistical mechanics of nonrelativistic fermions in a constant magnetic field is considered from the quantum field theory point of view. The fermionic determinant is computed using a general procedure that contains all possible…
We present an update on our on-going project to compute hadronic observables for Nf=2 flavours of O(a) improved Wilson fermions at small lattice spacings. The procedure to determine the lattice scale via the mass of the Omega baryon is…
As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…
We study the effective action associated to the Dirac operator in two dimensional non-commutative Field Theory. Starting from the axial anomaly, we compute the determinant of the Dirac operator and we find that even in the U(1) theory, a…
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of…
Given multiple orthogonal polynomials on the real line with respect to a system $\bm{\mu} = (\mu_1,\ldots,\mu_r)$, we investigate multiple orthogonal polynomials associated with any rational perturbation of the form $$…
It is recommended that lattice QCD representations of the fermion determinant, including the discretization of the Dirac operator, be checked in the continuum limit against known QED determinant results. Recent work on the massive QED…
We review results of the last two years concerning caloron solutions of unit charge with non-trivial holonomy, revealing the constituent monopole nature of these instantons. For SU(n) there are n such BPS constituents. New is the…
In the context of statistical physics, Chandrasekharan and Wiese recently introduced the \emph{fermionant} $\Ferm_k$, a determinant-like quantity where each permutation $\pi$ is weighted by $-k$ raised to the number of cycles in $\pi$. We…
We give the analytic result for the fermion zero-mode of the SU(2) calorons with non-trivial holonomy. It is shown that the zero-mode is supported on ONLY ONE of the constituent monopoles. We discuss some of its implications.
Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary…
A novel approach to S =1/2 antiferromagnets with strong fluctuations based on the representation of spin-1/2 operators as bylinear forms of real (Majorana) fermions is suggested. This representation has the advantage of being irreducible…
We introduce a new mathematical object, the "fermionant" ${\mathrm{Ferm}}_N(G)$, of type $N$ of an $n \times n$ matrix $G$. It represents certain $n$-point functions involving $N$ species of free fermions. When N=1, the fermionant reduces…
Efficiently bounding large determinants is an essential step in non-relativistic fermionic constructive quantum field theory to prove the absolute convergence of the perturbation expansion of correlation functions in terms of powers of the…
In this paper, we find several determinants expressing the Fibonomial coefficients. We also give the generating functions, Vandermonde identity, and continued fractions about Fibonomial coefficients.
The non-local dependence of the fermion determinant on the gauge field limits our ability of simulating Quantum Chromodynamics on the lattice. Here we present a factorization of the gauge field dependence of the fermion determinant based on…