TL;DR
This paper introduces q-regularization using q-deformed Hopf algebras to manage divergences in quantum field theory, demonstrating finite results for certain quantities when q differs from 1.
Contribution
It presents a novel approach to regularization in quantum field theory through q-deformation of Hopf algebras, providing a new mathematical framework.
Findings
Finite quantities for q ≠ 1 in q-deformed spaces
Divergences occur as q approaches 1
Application to λφ^4 theory illustrates the method
Abstract
An Introduction to Hopf algebras as a tool for the regularization of relavent quantities in quantum field theory is given. We deform algebraic spaces by introducing q as a regulator of a non-commutative and non-cocommutative Hopf algebra. Relevant quantities are finite provided q\neq 1 and diverge in the limit q\rightarrow 1. We discuss q-regularization on different q-deformed spaces for \lambda\phi^4 theory as example to illustrate the idea.
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