Related papers: A note on the Loop Formula for the fermionic deter…
This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…
The fermionant can be seen as a generalization of both the permanent (for $k=-1$) and the determinant. We demonstrate that it is VNP-complete for most cases. Furthermore it is #P-complete for the cases. The immanant is also a generalization…
We describe non-relativistic fermions on the lattice (Hubbard model) in the canonical formulation using transfer matrices in fixed fermion number sectors such that the partition function becomes fully factorized in time. By analytically…
In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for…
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…
Consider a one-parameter family of algebraic varieties degenerating to a reducible one. Our main result is a formula for the fundamental cycle of the limit subscheme of any family of effective Cartier divisors. The formula expresses this…
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static…
The canonical partition function approach was designed to avoid the overlap problem that affects the lattice simulations of nuclear matter at high density. The method employs the projections of the quark determinant on a fix quark number…
In a series of recent scientific contributions the role of bosonic and fermionic ladder operators in a macroscopic realm has been investigated. Creation, annihilation and number operators have been used in very different contexts, all…
Canonical differential calculus is defined for finitely generated abelian group with an involution existing consistently. Two such canonical calculi are found out. Fermionic representation for canonical calculus is defined based on…
We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.
We derive identities for the determinants of matrices whose entries are (rising) powers of (products of) polynomials that satisfy a recurrence relation. In particular, these results cover the cases for Fibonacci polynomials, Lucas…
We present the fermionic universal one--loop effective action obtained by integrating out heavy vector--like fermions at one loop using functional techniques. Even though previous approaches are able to handle integrating out heavy fermions…
The current status of bounds on and limits of fermion determinants in two, three and four dimensions in QED and QCD is reviewed. A new lower bound on the two-dimensional QED determinant is derived. An outline of the demonstration of the…
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…
Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory,…
It is possible to numerically solve QCD in the planar limit using standard numerical techniques on existing computer clusters. The basic ideas behind the computational strategy an recent numerical results in the fermionic sector of large N…
Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via…
The Wilson fermion determinant can be written in the form of a series expansion in fugacity $\xi=\exp(\mu/T)$, provided that the eigenmodes of the temporally reduced operator are obtained. Since the calculation of all eigenmodes rapidly…
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.