Related papers: Dyson-Schwinger equations in zero dimensions and p…
We discuss the Hamiltonian formulation of the Schwinger proper-time method of calculating Green functions in gauge theories. Instead of calculating Feynman diagrams, we solve the corresponding Dyson-Schwinger equations. We express the…
We provide an in-depth examination of the $GW$ approximation of Green's function many-body perturbation theory by detailing both its theoretical and practical aspects in the realm of quantum chemistry. First, the quasiparticle context is…
Exact solutions of classical gauge theories in even-dimensional (D=2n) spacetimes are discussed. Common and specific properties of these solutions are analyzed for the particular dimensions D=2, D=4, and D=6. A consistent formulation of…
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate…
We study the effective theory of slowly rotating black holes at the infinite limit of the spacetime dimension D. This large D effective theory is obtained by integrating the Einstein equation with respect to the radial direction. The…
In this study, we address the challenge of obtaining a Green's function operator for linear partial differential equations (PDEs). The Green's function is well-sought after due to its ability to directly map inputs to solutions, bypassing…
1+1 dimensional integrable quantum field theories correspond to a sparse subset of quantum field theories where the calculation of physically interesting observables can be brought to explicit, closed and manageable expressions thanks to…
We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for bound states in a basis set of finite size. We obtain two classes of solutions written as finite series of square integrable functions…
Two general unsolvability arguments for interacting bosonic quantum field theories are presented, based on Dyson-Schwinger equations on the lattice and cardinality considerations. The first argument is related to the fact that, on a lattice…
The purpose of this article is to develop a machinery to study the capacity of deep neural networks (DNNs) to approximate high-dimensional functions. In particular, we show that DNNs have the expressive power to overcome the curse of…
A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator,…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab inito problems with a fully realistic Hamiltonian in large basis sets…
An interesting feature of some open superstring models in $D < 10$ is the simultaneous presence, in the spectrum, of gauge fields and of a number of antisymmetric tensor fields. In these cases the Green-Schwarz mechanism can (and does) take…
We provide a systematic approach to compute different kinds of non-equilibrium Green's functions for open quantum systems which are essentially two-point correlation functions in time. We reveal that the definition of Green's functions…
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…
Green functions in a quantum field theory can be expanded as bivariate series in the coupling and a scale parameter. The leading logs are given by the main diagonal of this expansion, i.e. the subseries where the coupling and the scale…
This article establishes a complete approximate axiomatization for the real-closed field $\mathbb{R}$ expanded with all differentially-defined functions, including special functions such as $\sin(x), \cos(x), e^x, \dots$. Every true…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…