Mathematical Physics

1211 Submissions

[4] viXra:1211.0143 [pdf] replaced on 2014-04-19 05:52:35

Riemann Zeros and an Exponential Potential

Authors: Jose Javier Garcia Moreta
Comments: 10 Pages.

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue staircase includes the oscillatory and smooth part of the Number of Riemann zeros. In this paper and for simplicity we use units so 2m1  Keywords: = Riemann Hypothesis, WKB semiclassical approximation, exponential potential
Category: Mathematical Physics

[3] viXra:1211.0140 [pdf] submitted on 2012-11-24 02:12:29

The Poisson Realization of $\mathfrak{so}(2, 2k+2)$ on Magnetic Leave

Authors: Guowu Meng
Comments: 13 Pages.

Let ${\mathbb R}^{2k+1}_*={\mathbb R}^{2k+1}\setminus\{\vec 0\}$ ($k\ge 1$) and $\pi$: ${\mathbb R}^{2k+1}_*\to \mathrm{S}^{2k}$ be the map sending $\vec r\in {\mathbb R}^{2k+1}_*$ to ${\vec r\over |\vec r|}\in \mathrm{S}^{2k}$. Denote by $P\to {\mathbb R}^{2k+1}_*$ the pullback by $\pi$ of the canonical principal $\mathrm{SO}(2k)$-bundle $\mathrm{SO}(2k+1)\to \mathrm{S}^{2k} $. Let $E_\sharp\to {\mathbb R}^{2k+1}_*$ be the associated co-adjoint bundle and $E^\sharp\to T^*{\mathbb R}^{2k+1}_*$ be the pullback bundle under projection map $T^*{\mathbb R}^{2k+1}_*\to {\mathbb R}^{2k+1}_*$. The canonical connection on $\mathrm{SO}(2k+1)\to \mathrm{S}^{2k} $ turns $E^\sharp$ into a Poisson manifold. The main result here is that the real Lie algebra $\mathfrak{so}(2, 2k+2)$ can be realized as a Lie subalgebra of the Poisson algebra $(C^\infty(\mathcal O^\sharp), \{, \})$, where $\mathcal O^\sharp$ is a symplectic leave of $E^\sharp$ of special kind. Consequently, in view of the earlier result of the author, an extension of the classical MICZ Kepler problems to dimension $2k+1$ is obtained. The hamiltonian, the angular momentum, the Lenz vector and the equation of motion for this extension are all explicitly worked out.
Category: Mathematical Physics

[2] viXra:1211.0051 [pdf] replaced on 2013-04-02 13:59:43

A Note on Fractional Electrodynamics

Authors: Hosein Nasrolahpour
Comments: 7 Pages. A few formulas and references added.

We investigate the time evolution of the fractional electromagnetic waves by using the time fractional Maxwell's equations. We show that electromagnetic plane wave has amplitude which exhibits an algebraic decay, at asymptotically long times.
Category: Mathematical Physics

[1] viXra:1211.0048 [pdf] submitted on 2012-11-10 00:53:16

Zanaboni Theorem and Saint-Venant's Principle

Authors: Jian-zhong Zhao
Comments: 10 Pages.

Violating the law of energy conservation, Zanaboni Theorem is invalid and Zanaboni's proof is wrong. Zanaboni's mistake of " proof " is analyzed. Energy Theorem for Zanaboni Problem is suggested and proved. Equations and conditions are established in this paper for Zanaboni Problem, which are consistent with , equivalent or identical to each other. Zanaboni Theorem is, for its invalidity , not a mathematical formulation or proof of Saint-Venant's Principle. AMS Subject Classifications: 74-02, 74G50
Category: Mathematical Physics