Neutrix calculus I

Neutrix Calculus and Finite Quantum Field Theory

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT, obtaining finite renormaliza...

Neutrix Limit on Divergent Series

In this paper, we give a simple and straight forward definition for the neutrix limit of divergent series and use it to study the neutrix limits of the divergent series ralated to the Rieman-Zeta function ζ(α) and some series related to the polylogarith function Lin(z). Then, we apply the reults to some specific examles. Our reults on Riemann-Zeta function and its derivatives are consistent wit...

Commutative neutrix convolution products of functions

The commutative neutrix convolution product of the functions xe − and xe μx + is evaluated for r, s = 0, 1, 2, . . . and all λ, μ. Further commutative neutrix convolution products are then deduced.

Differential Calculus in Categories. I

The rewriting calculus - Part I

The ρ-calculus integrates in a uniform and simple setting first-order rewriting, λ-calculus and nondeterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T . In this first part, the calculus is motivated and its syntax and evaluation rules for any theory T are presented. In the syntactic case...