TL;DR
This paper introduces a novel series expansion for solving equations in quantum field theory using planar binary trees, providing explicit recursive formulas and exploring algebraic properties with applications to quantum electrodynamics.
Contribution
It presents a new series solution method for quantum field equations based on planar binary trees, with explicit recursive formulas and algebraic analysis.
Findings
Series expansion for quantum field equations using planar binary trees
Explicit recursive formulas for series terms
Applications to quantum electrodynamics propagators and Green functions
Abstract
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are investigated. Several examples are treated in the case of quantum electrodynamics: the complete fermion and photon propagators, the two-body Green function, and the one-body Green function in the presence of an external source, the complete vacuum polarization, electron self-energy and irreducible vertex.
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