相关论文: Green's function for a Schroedinger operator and s…
We present a simple recipe to construct the Green's function associated with a Hamiltonian of the form H=H_0+V, where H_0 is a Hamiltonian for which the associated Green's function is known and V is a delta-function potential. We apply this…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
A new method for non-perturbative calculation of Green functions in quantum mechanics and quantum field theory is proposed. The method is based on an approximation of Schwinger-Dyson equation for the generating functional by exactly soluble…
We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish…
The connection between the generating functions of various sets of tableaux and the appropriate families of quasisymmetric functions is a significant tool to give a direct analytical proof of some advanced bijective results and provide new…
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…
A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the…
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes.…
We find the generating functions for the Lagrangians of all-orders summable SU(2) Skyrmions. We then proceed to construct the explicit form of the Lagrangian, order by order in the derivatives of the pion field for two classes of models.
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate…
We develop calculational method for fermionic Green functions in the framework of Grassmann higher-order tensor renormalization group. The validity of the method is tested by applying it to three-dimensional free Wilson fermion system. We…
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
The availability of efficient Krylov subspace solvers play a vital role for the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new general numerical method to…
In a previous work [Andrade \textit{et al.}, Phys. Rep. \textbf{647}, 1 (2016)], it was shown that the exact Green's function (GF) for an arbitrarily large (although finite) quantum graph is given as a sum over scattering paths, where local…
Some elementary algebraic points regarding the Green function for a localised flux tube are developed. A calculation of the effective action density is included.
We present a new, highly efficient yet accurate approximation for the Green's functions of dressed particles, using the Holstein polaron as an example. Instead of summing a subclass of diagrams (e.g. the non-crossed ones, in the…
We consider gauge invariant quark two-point Green's functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional…
In this paper we establish a new summation method by expanding $\prod_{k}(1-\frac{z}{a_{k}})^{-1}$ with two approaches: the Taylor expansion and the infinite partial fraction decomposition. Here we focus on the case when $a_{k}$ is…
In this paper, we consider the set of r-symbols in a full generality. We construct Hall-Littlewood functions and Kostka functions associated to those r-symbols. We also discuss a multi-parameter version of those functions. We show that…