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A special integro-differential formula (SIDF) of the class of Green's theorems is established for a pair of functional forms (FFs) defined in a real affine Euclidean space of any given dimension n>=1 (nDRAES); one of the FFs is the Green FF…

A method for calculating the retarded Green's function for the gravitational wave equation in Friedmann-Roberson-Walker spacetimes, within the formalism of linearized Einstein gravity is developed. Hadamard's general solution to Cauchy's…

In this paper, we give a simple diagrammatic identification of the unique combination of the causal n-point vertex functions in the real time formalism that would coincide with the corresponding functions obtained in the imaginary time…

Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…

In physics, phenomena of diffusion and wave propagation have great relevance; these physical processes are governed in the simplest cases by partial differential equations of order 1 and 2 in time, respectively. By replacing the time…

Based on the closed time path formalism, a new Feynman rule for directly calculating the retarded and advanced Green functions is deduced. This Feynman rule is used to calculate the two-point self-energy and three-point vertex correction in…

In this work, the theory of second gradient electrodynamics, which is an important example of generalized electrodynamics, is proposed and investigated. Second gradient electrodynamics is a gradient field theory with up to second-order…

The retarded Green function for linear field perturbations of black hole spacetimes is notoriously difficult to calculate. One of the difficulties is due to a Dirac-$\delta$ divergence that the Green function possesses when the two…

The general relationship between a Retarded-Advanced Green function of the Real Time formalism and analytical continuations of the Imaginary Time Amplitude is obtained via perturbation theory. A 4-point R-A function is, at most, a linear…

The Green function (GF) related to the problem of a Dirac particle interacting with a plane wave and constant magnetic fields is calculated in the framework of path integral via Alexandrou et al. formalism according to the so-called global…

Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…

We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…

A formulation for the efficient calculation of the electromagnetic retarded potential generated by time-dependent electron density in the context of real-time time dependent density functional theory (RT-TDDFT) is presented. The electron…

We show how the linearized equations of motion of any dissipative current are determined by the analytical structure of the associated retarded Green's function. If the singularity of the Green's function, which is nearest to the origin in…

Both theoretical and numerical studies of the Kuramoto-Sivashinsky equation have mostly considered periodic boundary conditions. In this setting, the Fourier decomposition of the solution is central to theoretical ideas, such as…

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…

This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…

A new integral identity for functions with continuous second partial derivatives is derived. It is shown that the value of any function f(r,t) at position r and time t is completely determined by its previous values at all other locations…

We propose a general framework for computing Retarded Green's Functions (RGFs) on quantum computers by recasting their evaluation as a problem of circuit differentiation. Our proposal is based on real-time evolution and specifically…

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…