Analytical Solution Of Complete Schwarzschild\'s Planetary Equation

An analytical solution of Monge differential equation

We present the exact solution to the non linear Monge differential equation λ(x, t)λx(x, t) = λt(x, t). It is widely accepted that the Monge equation is equivalent to the ODE .. X= 0 of free motion for particular conditions. Furthermore, the Monge Type equations are connected withX = F ( . X, X; t), which can be integrated with quadratures [1]. Other asymptotic solutions are discussed, see e.g....

Instantaneous Bethe–salpeter Equation: Improved Analytical Solution

Studying the Bethe–Salpeter formalism for interactions instantaneous in the rest frame of the bound states described, we show that, for bound-state constituents of arbitrary masses, the mass of the ground state of a given spin may be calculated almost entirely analytically with high accuracy, without the (numerical) diagonalization of the matrix representation obtained by expansion of the solut...

Instantaneous Bethe–salpeter Equation: (semi-)analytical Solution

The Bethe–Salpeter equation for bound states of a fermion–antifermion pair in the instantaneous approximation for the involved interaction kernel is converted into an equivalent matrix eigenvalue problem with explicitly (algebraically) given matrices. PACS numbers : 11.10.St, 03.65.Ge ∗ E-mail address : [email protected] ‡ E-mail address : [email protected] † E-mail address : franz.schoebe...

Semi-analytical Solution of Dirac equation in Schwarzschild Geometry

Analytical solution of the radiative transfer equation for polarized light

A new formalism is introduced for the transfer of polarized radiation. Stokes parameters are shown to be four– vectors in a Minkowski-like space and, most strikingly, the radiative transfer equation (RTE) turns out to be an infinitesimal transformation under the Poincaré (plus dilatations) group. A solution to the transfer equation as a finite element of this group is proposed.