Coalgebras and quantization

TL;DR

This paper explores two coalgebra structures in quantum field theory, one related to deformation quantization and the other to renormalization, providing a mathematical framework for these processes.

Contribution

It introduces and analyzes two distinct coalgebra structures within quantum field theory, linking them to quantization and renormalization processes.

Findings

Coalgebra in Hopf algebra leads to deformation quantization.

Co-module coalgebra over Hopf algebra defines chronological products.

Framework connects coalgebra structures to quantum field theory processes.

Abstract

Two coalgebra structures are used in quantum field theory. The first one is the coalgebra part of a Hopf algebra leading to deformation quantization. The second one is a co-module co-algebra over the first Hopf algebra and it is used to define connected chronological products and renormalization.