Related papers: Fermionic determinant for dyons and instantons wit…
We review the resolvent technique for computing the effective action in planar QED. For static magnetic backgrounds the effective action yields (minus) the effective energy of the fermions, while for electric backgrounds the imaginary part…
A form in a polynomial ring over a field is said to be homaloidal if its polar map is a Cremona map, i.e., if the rational map defined by the partial derivatives of the form has an inverse rational map. The object of this work is the search…
The fermion determinant in four-dimensional quantum electrodynamics in the presence of O(2)XO(3) symmetric background gauge fields with a nonvanishing global chiral anomaly is considered. It is shown that the leading mass singularity of the…
We use proper-time regularizations to define the one-loop fermion determinant in the form suggested by Gasser and Leutwyler some years ago. We show how to obtain the polynomial by which this definition of ln det D needs to be modified in…
Determinantal point processes are characterized by a special structural property of the correlation functions: they are given by minors of a correlation kernel. However, unlike the correlation functions themselves, this kernel is not…
We consider the five-vertex model on a finite square lattice with fixed boundary conditions such that the configurations of the model are in a one-to-one correspondence with the boxed plane partitions (3D Young diagrams which fit into a box…
The Gelfand-Yaglom formula relates functional determinants of the one-dimensional second order differential operators to the solutions of the corresponding initial value problem. In this work we generalise the Gelfand-Yaglom method by…
Representation of a $D$-dimensional fermion determinant as a path integral of exponent of a $(D+1)$-dimensional Hermitean bosonic action is constructed.
We derive an exact formula for the field form factor in the anyonic Lieb-Liniger model, valid for arbitrary values of the interaction $c$, anyonic parameter $\kappa$, and number of particles $N$. Analogously to the bosonic case, the form…
The topology of two-dimensional movement allows for existing of anyons -- particles obeying statistics intermediate between that of bosons and fermions. In this article, the functional form of the occupation numbers of free anyons is…
We present determinantal formulas for families of exceptional $X_m$-Laguerre and exceptional $X_m$-Jacobi polynomials and also for exceptional $X_2$-Hermite polynomials. The formulas resemble Vandermonde determinants and use the zeros of…
The aim of this paper is to offer an algebraic construction of infinite-dimensional Grassmannians and determinant bundles (and therefore valid for arbitrary base fields). As an application we construct the $\tau$-function and formal…
We consider the rational six-vertex model on an L-by-L lattice with domain wall boundary conditions and restrict N parallel-line rapidities, N < L/2, to satisfy length-L XXX spin-1/2 chain Bethe equations. We show that the partition…
We use the Whittaker vectors and the Drinfeld Casimir element to show that eigenfunctions of the difference Toda Hamiltonian can be expressed via fermionic formulas. Motivated by the combinatorics of the fermionic formulas we use the…
Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive…
We give a simple formula for some determinants, and an analogous formula for pfaffians, both of which are polynomial identities. The second involve some expressions that interpolate between determinants and pfaffians. We give several…
For an ergodic measure preserving action on a probability space, consider the corresponding crossed product von Neumann algebra. We calculate the Fuglede-Kadison determinant for a class of operators in this von Neumann algebra in terms of…
We show that $QCD_2$ with adjoint fermions involves instantons due to nontrivial $\pi_1[SU(N)/Z_N]~=~Z_N$. At high temperatures, quasiclassical approximation works and the action and the form of effective (with account of quantum…
We analyze the fluctuations in the case of mass reweighting for N_f=2 Wilson fermions. We use a domain decomposition factorization of the fermion determinant. Ratios of determinants are estimated stochastically. We study the stochastic and…
We present a calculation of the leading order hadronic contribution to the anomalous magnetic moment of the muon for a dynamical simulation of 2+1 flavour QCD using domain wall fermions. The electromagnetic 2-point function is evaluated on…