Quantum Clifford Hopf Gebra for Quantum Field Theory

TL;DR

This paper advocates for using Quantum Clifford Hopf Gebras in quantum field theory, highlighting their potential to improve diagrammatic calculus and regularization methods.

Contribution

It introduces Quantum Clifford Hopf Gebras as a novel mathematical framework for quantum field theory, emphasizing their role in diagram interpretation and regularization.

Findings

Reinterprets Feynman diagrams as graphical tangles.

Proposes convolution Hopf Gebras for regularization.

Highlights the importance of the antipode in the framework.

Abstract

We give arguments for the necessity to employ Quantum Clifford Hopf Gebras in quantum field theory. The role of the antipode is examined, Feynman diagrams are re-interpreted as tangles of graphical calculus. Regularization due to the design of convolution Hopf gebras is given as a program for further research.