Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory
Matilde Marcolli, Alexander Port
TL;DR
This paper establishes a connection between graph grammars, Lie algebras, and quantum field theory, revealing that Feynman graphs can be generated by specific graph grammars, bridging formal language theory and physics.
Contribution
It introduces a novel association of Lie algebras to classes of graph grammars and links Feynman graphs to graph languages generated by graph grammars.
Findings
Lie algebras associated with certain graph grammars resemble insertion Lie algebras in quantum field theory
Feynman graphs can be generated by graph grammars specific to quantum field theories
The work bridges formal language theory and quantum physics through graph structures
Abstract
Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a Lie algebra, whose structure is reminiscent of the insertion Lie algebras of quantum field theory. We also show that the Feynman graphs of quantum field theories are graph languages generated by a theory dependent graph grammar.
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Taxonomy
TopicsGraph Theory and Algorithms · Model-Driven Software Engineering Techniques · Parallel Computing and Optimization Techniques