Related papers: Fermionic partition functions for a periodic solit…
We derive a boson Hamiltonian from a Nuclear Hamiltonian whose potential is expanded in pairing multipoles and determine the fermion-boson mapping of operators. We use a new method of bosonization based on the evaluation of the partition…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while…
In the last few years it has been proposed a one-dimensional factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a block-local action of the auxiliary bosonic fields. Here we propose a…
We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We…
Based on the chiral symmetry breaking pattern and the corresponding low-energy effective lagrangian, we determine the fermion mass dependence of the partition function and derive sum rules for eigenvalues of the QCD Dirac operator in finite…
We present a new method of bosonization of fermion systems applicable when the partition function is dominated by composite bosons. Restricting the partition function to such states we get an euclidean bosonic action from which we derive…
We reconsider the procedure of calculation of fermion-boson vertices and numerical solution of Bethe-Salpeter equations, used in non-local extensions of dynamical mean-field theory. Because of the frequency dependence of vertices, finite…
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions,…
We give a direct proof of the combinatorial formula for interpolation Macdonald polynomials by introducing certain polynomials, which we call generic Macdonald polynomials, which depend on $d$ additional parameters and specialize to all…
Recently, Boole polynomials have been studied by Kim and Kim over the p-adic number field. In this paper, we consider a q-extension of Boole polynomials by using the fermionic p-adic integrals on Zp and give some new identities related to…
The Fermi function $F(Z,E)$ accounts for QED corrections to beta decays that are enhanced at either small electron velocity $\beta$ or large nuclear charge $Z$. For precision applications, the Fermi function must be combined with other…
We employ a discrete integral-reflection representation of the double affine Hecke algebra of type $C^\vee C$ at the critical level q=1, to endow the open finite $q$-boson system with integrable boundary interactions at the lattice ends. It…
The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The…
This paper is the first in the series devoted to evaluation of the partition function in statistical models on graphs with loops in terms of the Berezin/fermion integrals. The paper focuses on a representation of the determinant of a square…
We use Schwinger's formula, introduced by himself in the early fifties to compute effective actions for QED, and recently applied to the Casimir effect, to obtain the partition functions for both the bosonic and fermionic harmonic…
Kostant's partition function counts the number of ways to represent a particular vector (weight) as a nonnegative integral sum of positive roots of a Lie algebra. For a given weight the $q$-analog of Kostant's partition function is a…
We investigate combinatorics of the instanton partition function for the generic four dimensional toric orbifolds. It is shown that the orbifold projection can be implemented by taking the inhomogeneous root of unity limit of the q-deformed…
We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using…
We give a self-contained exposition of the combinatorial solution of quantum mechanical systems of coupled spins on a one-dimensional lattice. Using Trotter formula, we write the partition function as a generating function of a spanning…
In this paper, we show some expressions of certain $q$-multiple zeta-star values at roots of unity. These explicit formulas are expressed by using the determinants or Bell polynomials. Explicit formulas for other types of values can be…