Fundamental Solution of Laplace's Equation in Hyperspherical Geometry

Fundamental Solution of Laplace’s Equation in Hyperspherical Geometry

Due to the isotropy of d-dimensional hyperspherical space, one expects there to exist a spherically symmetric fundamental solution for its corresponding Laplace–Beltrami operator. The R-radius hypersphere SR with R > 0, represents a Riemannian manifold with positive-constant sectional curvature. We obtain a spherically symmetric fundamental solution of Laplace’s equation on this manifold in ter...

Solution of Vacuum Field Equation Based on Physics Metrics in Finsler Geometry and Kretschmann Scalar

The Lemaître-Tolman-Bondi (LTB) model represents an inhomogeneous spherically symmetric universefilledwithfreelyfallingdustlikematterwithoutpressure. First,wehaveconsideredaFinslerian anstaz of (LTB) and have found a Finslerian exact solution of vacuum field equation. We have obtained the R(t,r) and S(t,r) with considering establish a new solution of Rµν = 0. Moreover, we attempttouseFinslergeo...

Solution of a Linearized Model of Heisenberg’s Fundamental Equation Ii

Abstract. We propose to look at (a simplified version of) Heisenberg’s fundamental field equation (see [2]) as a relativistic quantum field theory with a fundamental length, as introduced in [1] and give a solution in terms of Wick power series of free fields which converge in the sense of ultrahyperfunctions but not in the sense of distributions. The solution of this model has been prepared in...

Semi-analytical Solution of Dirac equation in Schwarzschild Geometry

Solution of Dirac's equation in Reissner-Nordström geometry.

The nature of the singularity at the origin of the solution of Dirac's equation in Reissner-Nordström geometry is different from that in flat space. Here, both independent solutions are regular at the origin, and both give a convergent normalization integral. The choice between the two solutions is made by requiring that the variational integral, from which the differential equation can be deri...