# Mathematical Physics

## 1009 Submissions

[2] **viXra:1009.0047 [pdf]**
*replaced on 2013-05-03 15:35:33*

### Summary of the Zeta Regularization Method Applied to the Calculation of Divergent Series and Divergent Integrals

**Authors:** Jose Javier Garcia Moreta

**Comments:** 20 Pages.

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization
•Keywords: = Riemann Zeta function, Functional determinant, Zeta regularization, divergent series .

**Category:** Mathematical Physics

[1] **viXra:1009.0007 [pdf]**
*replaced on 2012-03-21 15:41:57*

### A Multiple Particle System Equation Underlying the Klein-Gordon-Dirac-Schrödinger Equations

**Authors:** DT Froedge

**Comments:** 36 Pages. V032112 ongoing

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are, and single particle special cases. The basic concept is that there is a broader picture, based on a more general equation that includes the entire system of particles. The first part will be to postulate an equation, and then, by then by defining an action field based on the endpoint action of the particles in the system, develop a solution which properly illustrates internal dynamics as well as particle interactions. The complete function has both real, and imaginary, as well as timelike and spacelike parts, each of which are separable into independent expressions that define particle properties. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an atomic system, particle masses are eigenvalues in an interacting universe of particles. The Dirac massive and massless equation and solution will be shown as factorable independent parts of the Systemfunction. A clear relation between the classical and quantum properties of particles is made, increasing the scope of QM.

**Category:** Mathematical Physics