# Mathematical Physics

## 1007 Submissions

[2] **viXra:1007.0031 [pdf]**
*submitted on 19 Jul 2010*

### A New Generic Class of Beltrami "Force-Free" Fields. Part-I: Theoretical Considerations

**Authors:** T. E. Raptis

**Comments:** 13 pages.

We report on a new general class of solutions of the Beltrami equation, with
special characteristics. We also provide examples of solutions that also satisfy Maxwell equations.
A subset of these solutions can be isolated which corresponds to "gauge" fields. A special
projective geometry of vacuum fields is also revealed and discussed.

**Category:** Mathematical Physics

[1] **viXra:1007.0005 [pdf]**
*replaced on 2012-11-22 05:57:29*

### A Hamiltonian Whose Energies Are the Zeros of the Riemann XI Function

**Authors:** Jose Javier Garcia Moreta

**Comments:** 12 Pages.

· ABSTRACT: We give a possible interpretation of the Xi-function of Riemann as the
Functional determinant det ( E - H ) for a certain Hamiltonian quantum operator in
one dimension
2
2 d V (x)
dx
- + for a real-valued function V(x) , this potential V is
related to the half-integral of the logarithmic derivative for the Riemann Xi-function,
through the paper we will assume that the reduced Planck constant is defined in units
where h =1 and that the mass is 2m =1.In this case the Energies of the Hamiltonian
operator will be the square of the imaginary part of the Riemann Zeros 2
n n E =g Also
trhough this paper we may refer to the Hamiltonian Operator whose Energies are the
square of the imaginary part of the Riemann Zeros as H or 2 H (square) in the same
case we will refer to the potential inside this Hamiltonian either as 2 V (x) or V (x) to
simplify notation.
· Keywords: = Riemann Hypothesis, Functional determinant,

**Category:** Mathematical Physics