Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology
Christoph Bergbauer, Dirk Kreimer
TL;DR
This paper reviews how Hochschild cohomology of renormalization Hopf algebras informs the understanding of locality and Dyson-Schwinger equations in quantum field theories.
Contribution
It highlights the role of Hochschild cohomology in analyzing the structure of renormalization Hopf algebras and their connection to local quantum field theories.
Findings
Hochschild cohomology relates to the locality property in quantum field theories.
It provides insights into Dyson-Schwinger equations within the Hopf algebra framework.
The review emphasizes the mathematical structure underlying renormalization processes.
Abstract
In this review we discuss the relevance of the Hochschild cohomology of renormalization Hopf algebras for local quantum field theories and their equations of motion.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Operator Algebra Research