TL;DR
This paper reviews the algebraic approach to quantum field theory using Hopf algebras and Hochschild cohomology, highlighting its mathematical foundations and potential for advancing understanding.
Contribution
It consolidates scattered algebraic structures related to quantum fields into a unified framework, emphasizing their mathematical significance.
Findings
Identification of key algebraic structures in quantum field theory
Clarification of the role of Hopf algebras and Hochschild cohomology
Potential avenues for further mathematical development
Abstract
We give an account of the current state of the approch to quantum field theory via Hopf algebras and Hochschild cohomology. We emphasize the versatility and mathematical foundation of this algebraic structure, and collect algebraic structures here in one place which are either scattered over the literature, or only implicit in previous writings. In particular we point out mathematical structures which can be helpful to farther develop our mathematical understanding of quantum fields.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology