Semiring Parsing the S-Matrix: Packed forests, recursion as dynamic programming, and typed pruning in perturbative field theory

Summary and scope

A computational account of how typed grammars, packed forests and dynamic programming can organise perturbative amplitude calculations for supplied field-theory rules. The examples distinguish diagram syntax from the algebra used to evaluate it. Their scope does not select a physical Lagrangian, determine interaction coefficients or certify every loop calculation. The contribution is the parsing and evaluation method within its stated examples.

Keywords

How to cite

Elliman, D. (2026). Semiring Parsing the S-Matrix: Packed forests, recursion as dynamic programming, and typed pruning in perturbative field theory. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21204128

@techreport{elliman2026semiringparsingsmatrix,
  author      = {Elliman, David},
  title       = {Semiring Parsing the S-Matrix: Packed forests, recursion as dynamic programming, and typed pruning in perturbative field theory},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21204128},
  url         = {https://neusym.ai/papers/semiring_parsing_smatrix/}
}