Finite-Order Truncation and the Physical Interpretation of Feynman Diagrams: A Problem of Process-Representation Completeness in Quantum Field Theory
Abstract
Feynman diagrams occupy an ambiguous position in quantum field theory (QFT). They are mathematically defined devices for generating perturbative contributions, but they are also routinely interpreted through narratives of particle emission, absorption, exchange, and virtual-particle interaction. An important tension arises from the difference between the unbounded family of diagrams admitted by perturbative rules and the finite collection of diagrams retained in actual calculations. This tension can be formulated without assuming that the perturbation series diverges. If Feynman diagrams are interpreted as representations of possible microscopic physical processes, what justifies the transition from an unbounded diagrammatic domain to a finite-order computational result? In particular, what does the success of a finite perturbative approximation establish about the physical processes represented by the diagrams it retains and omits?
This paper develops the concept of a finite-order process-representation gap. The gap arises when a finite-order calculation is assigned a physical-process interpretation whose apparent scope extends to an unbounded family of diagrammatically admissible processes, without an explicit account of the relationship between diagrammatic admissibility, physical possibility, process-level completeness, and observable-level accuracy. The argument does not establish that finite-order perturbation theory is mathematically invalid, nor does it imply that a finite approximation cannot be accurate. Instead, it distinguishes computational adequacy from ontological and explanatory completeness. It further identifies three possible responses: restricting the representational claims of Feynman diagrams, supplying an explicit rule connecting diagrammatic truncation with the physical target, or adopting a non-literal account of virtual processes. Divergent perturbation series can intensify the problem, but divergence is not a premise of the argument. The proposed contribution is a conceptual refinement of existing debates concerning Feynman diagrams, rather than a claim to have discovered the general problem of their physical interpretation.
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BibTeX
@misc{sulin2026finiteorder,
title = {{Finite-Order Truncation and the Physical Interpretation of Feynman Diagrams: A Problem of Process-Representation Completeness in Quantum Field Theory}},
author = {Zhang Sulin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23608867},
url = {https://zenodo.org/records/23608867},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite-Order Truncation and the Physical Interpretation of Feynman Diagrams: A Problem of Process-Representation Completeness in Quantum Field Theory
AU - Zhang Sulin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23608867
UR - https://zenodo.org/records/23608867
AB - Feynman diagrams occupy an ambiguous position in quantum field theory (QFT). They are mathematically defined devices for generating perturbative contributions, but they are also routinely interpreted through narratives of particle emission, absorption, exchange, and virtual-particle interaction. An important tension arises from the difference between the unbounded family of diagrams admitted by perturbative rules and the finite collection of diagrams retained in actual calculations. This tension can be formulated without assuming that the perturbation series diverges. If Feynman diagrams are interpreted as representations of possible microscopic physical processes, what justifies the transition from an unbounded diagrammatic domain to a finite-order computational result? In particular, what does the success of a finite perturbative approximation establish about the physical processes represented by the diagrams it retains and omits? This paper develops the concept of a finite-order process-representation gap. The gap arises when a finite-order calculation is assigned a physical-process interpretation whose apparent scope extends to an unbounded family of diagrammatically admissible processes, without an explicit account of the relationship between diagrammatic admissibility, physical possibility, process-level completeness, and observable-level accuracy. The argument does not establish that finite-order perturbation theory is mathematically invalid, nor does it imply that a finite approximation cannot be accurate. Instead, it distinguishes computational adequacy from ontological and explanatory completeness. It further identifies three possible responses: restricting the representational claims of Feynman diagrams, supplying an explicit rule connecting diagrammatic truncation with the physical target, or adopting a non-literal account of virtual processes. Divergent perturbation series can intensify the problem, but divergence is not a premise of the argument. The proposed contribution is a conceptual refinement of existing debates concerning Feynman diagrams, rather than a claim to have discovered the general problem of their physical interpretation.
ER -