Related papers: The Green function for thermal waves induced by at…
We consider a one-dimensional gas of spin-1/2 fermions interacting through $\delta$-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point…
Gravitational wave solutions to Einstein's equations and their generation are examined in D-dimensional flat spacetimes. First the plane wave solutions are analyzed; then the wave generation is studied with the solution for the metric…
The thermal Wightman functions for free, massless particles of spin 0, 1/2, 1, 3/2, and 2 are computed directly in coordinate space by solving the appropriate differential equation and imposing the Kubo-Martin-Schwinger condition. The…
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral…
In this paper the heat waves, induced by ultra-short laser pulses are considered. The hyperbolic heat transport in n-dimensional space-time is formulated and solved. It is shown that only for n-odd for heat waves the Huygens principle is…
The pointwise space-time behavior of the Green's function of the one-dimensional Vlasov-Maxwell-Boltzmann (VMB) system is studied in this paper. It is shown that the Green's function consists of the macroscopic diffusive waves and Huygens…
Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these…
A general approach for derivation of the spectral relations for the multitime correlation functions is presented. A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
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…
A method is given to obtain the Green's function for the Poisson equation in any arbitrary integer dimension under periodic boundary conditions. We obtain recursion relations which relate the solution in d-dimensional space to that in…
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…
The three-dimensional Klein-Gordon oscillator is shown to exhibit an algebraic structure known from supersymmetric quantum mechanics. The supersymmetry is found to be unbroken with a vanishing Witten index, and it is utilized to derive the…
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…
A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence…
Using a path integral approach and bosonization, we calculate the low energy asymptotics of the one particle Green's function for a ``magnetically incoherent'' one dimensional strongly interacting electron gas at temperatures much greater…
Minimal length of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
We show that the Green's function of a two dimensional fermion with a modified dispersion relation and short distance parameter $a$ is given by the Lerch zeta function. The Green's function is defined on a cylinder of radius R and we show…
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…