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Jose Javier Garcia Moreta

Publications and source records attributed to Jose Javier Garcia Moreta.

5 recordsLinked to original sources
arXiv2007

A New Approach to Renormalization, Using Zeta regularization

In this paper we present a method to deal with divergences in perturbation theory using the method of the Zeta regularization, first of all we use the Euler-Mc Laurin Sum formula to associate the divergent integral to a divergent sum in the form 1+2^{m}+3^{m}+... After that we find a recurrence formula for the integrals and apply zeta regularization techniques to obtain finite results for the divergent series. (Through all the paper we use the notation m, for the power of the modulus of p, so we must not confuse it with the value of the mass of the quantum particle) changes: added Bibliography about ramanujan Resummation and references of Zeta regularization in Hardy,s Book "divergent series".

math.GM↗
arXiv2007

An Approach to PI(x) and other Arithmetical function by Variational principles

In this paper we present a method to derive Pi(x) and other Arithemtical functions that can be generated by a Dirichlet series by variational principles,we use a variational method to determine the solution for a Fredholm integral equation of second kind, after that we propose (obtain) two integral equations one for the Pi(x) and other for the arithmetical function A(x)=Sum(n,x)a(n) so they can be solved by usual optimization method. Also some conjectures on the value for the asymptotic value of the sum of f(t)=t^{n} are given in the form Li(x^{n+1}) Changes: Rayleigh-ritz Variational Methods added, we have also included a brief description of how to accelerate the convergence of the series Sum{p}f(x),Grammar changes.

math.GM↗
arXiv2007

Evaluation of Functional Integrals by means of series and the method of Borel transform

In this paper I give an evaluation of a functional integral by means of a series in functional derivatives, first of all we propose a differential equation of first order and solve it by iterative methods, to obtain a series for the indefinite integral in one dimension, after that we extend this concept to infinite dimensional spaces, we introduce the functional derivative and propose a functional differential equation for the functional integral which we solve by iteration obtaining a series that includes the n-th order functional derivative dn, this series can be improved by using the Euler transform for alternating series. Also in the second part we study an evaluation of the Path integral using Saddle-point methods, the corrections to the WKB approach that yield to a divergent series are evaluate by means of a Borel transform, to accelerate its convergence we use the Abel-Euler algorithm for power series.

math.GM↗
arXiv2007

Quantization of Arbitrary Hamiltonians

In this paper we discuss a method to apply Quantization rules for arbitrary Hamiltonians that are not necessarily Polynomials in variable p, so we have H of the form H(x,p)=F(x,p)+g(x) the method uses the results of "Fractional Calculus" for derivatives and integrals.

math.GM↗