Related papers: Discussion of the loop formula for the fermionic d…
We derive the fermion loop formulation for the supersymmetric nonlinear O$(N)$ sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over…
We present an explicit formula for computing toric residues as a quotient of two determinants, a la Macaulay, where the numerator is a minor of the denominator. We also give an irreducible representation of toric residues by extending the…
A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of…
We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves…
We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct…
The use of known analytic results for the continuum fermion determinants in QCD and QED as benchmarks for zero lattice spacing extrapolations of lattice fermion determinants is proposed. Specifically, they can be used as a check on the…
Within the Hamiltonian formulation of Lattice gauge theories, prepotentials, belonging to the fundamental representation of the gauge group and defined locally at each site of the lattice, enables us to construct local loop operators and…
We compute quaisideterminants and determinants of quaternionic matrices
It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I…
This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.
We give solutions of a Diophantine equation containing factorials, which can be written as a cubic form, or as a sum of binomial coefficients. We also give some solutions to higher degree forms and relate some solutions to an unsolvable…
Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an…
The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity…
Infinite order linear recurrences are studied via kneading matrices and kneading determinants. The concepts of kneading matrix and kneading determinant of an infinite order linear recurrence, introduced in this work, are defined in a purely…
We evaluate the fermionic determinant for massless QED_2 at finite temperature, in the imaginary time formalism. By using a decoupling transformation of the fermionic fields, we show that the determinant factorizes into the usual,…
We give a new proof of the fact that any finite quadratic module can be decomposed into indecomposable ones. For any indecomposable finite quadratic module, we construct a lattice, and a positive definite lattice, both of which are of the…
The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.
A formula is presented for the determinant of the second additive compound of a square matrix in terms of coefficients of its characteristic polynomial. This formula can be used to make claims about the eigenvalues of polynomial matrices,…
We present determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.
In contrast to the determinant, no algorithm is known for the exact determination of the permanent of a square matrix that runs in time polynomial in its dimension. Consequently, non interacting fermions are classically efficiently…