Feynman-diagram loop counting University Quantum Field Theory I · Scalar φ⁴ diagrams
Vertex Forge
Add interaction vertices and internal propagators to satisfy a connected diagram's loop order.
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Four-point tree
A quartic vertex has four line ends. Each internal propagator consumes two ends and each external leg consumes one.
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Forge a connected four-point count with zero loops.
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Use leg counting and connected-graph topology to identify the loop count and coupling order of scalar phi-four diagrams.
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The physics behind the game
Use leg counting and connected-graph topology to identify the loop count and coupling order of scalar phi-four diagrams.
4V = 2I + E; L = I − V + 1; coupling order λⱽ
Model assumptions. Connected diagrams in scalar φ⁴ theory in four spacetime dimensions, with V ≥ 1 and no extra vertex types. Counts must leave four line ends per vertex and a nonnegative connected loop number. The drawing is representative count bookkeeping, not a unique graph or a spacetime trajectory. Tadpoles and multiple internal lines are allowed; amplitudes, symmetry factors and scattering rates are not computed.