Related papers: An explicit Koppelman formula for $dd^c$ and Green…
We consider the two-dimensional non-relativistic Coulomb problem with the aid of the momentum space construction of the associated Green's function. Our presentation has precursors in three dimensions. It is mainly Schwinger's approach…
From perturbation theory, Green's functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order…
We present a further development of methods for analytical calculations of Green's functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we…
In this paper, we first describe how to find the generating function for the sum of the areas under generalized Dyck paths (with an arbitrary set of steps) using Motzkin paths as a motivating example. We then focus on Motzkin and Dyck…
We present two methods for computing two-time correlation functions or Green's functions from real time bold-line continuous time quantum Monte Carlo. One method is a formally exact generalized auxiliary lead formalism by which spectral…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…
In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the…
Homogeneous and inhomogeneous biharmonic equation are considered on the $n$-dimensional unit sphere. The Green function is given as a series of Gegenbauer polynomials. In the paper, explicit representations of the Green function are found…
Exact solutions of Dirac equation in two spatial dimensions in the Coulomb field are obtained. Equation which determines the so-called critical charge of the Coulomb field is derived and solved for a simple model.
In this paper, we study the polyatomic Boltzmann equation based on continuous internal energy, focusing on physically relevant collision kernels of the hard potentials type with integrable angular part. We establish three main results:…
We provide explicit formulas for the Green function of an elliptic PDE in the infinite strip and the half-plane. They are expressed in elementary and special functions. Proofs of uniqueness and existence are also given.
The exact Green function is constructed for a quantum system, with known Green function, which is decorated by two delta function impurities.It is shown that when two such impurities coincide they behave as a single singular potential with…
We compute the strong coupling constant $g_{P^* P \pi}$, with $P$ and $P^*$ respectively pseudoscalar and vector heavy mesons by using the QCD sum rules approach. Our computation is based on the evaluation of the time ordered product of…
We construct the Hadamard Green's function by using the eigenfunction, which are obtained by solving the wave equation for the massless conformal scalar field on the S^n-1 of a n-dimensional closed, static universe. We also consider the…
We study Green's matrices for divergence form, second order strongly elliptic systems with bounded measurable coefficients in two dimensional domains. We establish existence, uniqueness, and pointwise estimates of the Green's matrices.
We construct Koppelman formulas on Grassmannians for forms with values in any holomorphic line bundle as well as in the tautological vector bundle and its dual. As a consequence we obtain some vanishing theorems of the Bott-Borel-Weil type.…
A simple integral representation is derived for the quasiclassical Green function of the Dirac equation in an arbitrary spherically-symmetric decreasing external field. The consideration is based on the use of the quasiclassical radial wave…
We demonstrate that the effective Hamiltonians obtained with the downfolding procedure based on double unitary coupled cluster (DUCC) ansatz can be used in the context of Greens function coupled cluster (GFCC) formalism to calculate…