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The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…
We obtain a complete series solution of stationary Schr\"odinger's equation in the general quantum systems. It is exact in the sense that any approximation means is not used, or that the whole corrections or contributions from all order…
Free-particle Green's function plays a central role in the theoretical description of electron scattering and autoionization processes in quantum physics and chemistry. Recently, Gaussian basis set approaches have become increasingly…
We derive a systematic procedure to compute Green functions for the massive Schwinger model via a perturbation expansion in the fermion mass. The known exact solution of the massless Schwinger model is used as a starting point. We compute…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
We construct retarded and advanced Green's functions for gravitational perturbations in Kerr in an ingoing radiation gauge. Our Green's functions have a frequency domain piece that has previously been obtained by Ori [Phys. Rev. D 67…
Inspired by the recent proposed Legendre orthogonal polynomial representation of imaginary-time Green's functions, we develop an alternate representation for the Green's functions of quantum impurity models and combine it with the…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…
It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of…
A derivation is given of the Feynman rules to be used in the perturbative computation of the Green's functions of a generic quantum many-body theory when the action which is being perturbed is not necessarily quadratic. Some applications…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
The electromagnetic Green's function is expressed from the inverse Helmholtz operator, where a second frequency has been introduced as a new degree of freedom. The first frequency results from the frequency decomposition of the…
The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into…
We derive the quantum effective action up to second order in gradients and up to two-loop order for an interacting scalar field theory. This expansion of the effective action is useful to study problems in cosmological settings where…
We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a…
We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact…
We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…