Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
Adrian Tanasa
TL;DR
This paper reviews how combinatorial Hopf algebras underpin the renormalization process in quantum field theories, focusing on both commutative and noncommutative models like the Grosse-Wulkenhaar model.
Contribution
It provides a comparative analysis of algebraic structures in commutative and noncommutative quantum field theories, highlighting their role in renormalization.
Findings
Hopf algebras facilitate renormalization in quantum field theory.
The noncommutative Grosse-Wulkenhaar model is analyzed using these algebraic tools.
Abstract
We briefly review the r\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative Grosse-Wulkenhaar model.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Algebraic structures and combinatorial models · Advanced Topics in Algebra