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Published December 2015 | public
Journal Article Open

Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory


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.

Additional Information

© 2015 Springer Basel. Received: 11 March 2015; Accepted: 14 May 2015; Published online: 13 August 2015. The first author is supported by NSF Grants DMS-1007207, DMS-1201512, PHY-1205440. The second author was supported by a Summer Undergraduate Research Fellowship at Caltech.

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August 22, 2023
August 22, 2023