Lesson 1 — φ⁴ field-strength renormalization & systematics of UV divergences · P1

Physics

Problem

Consider a scalar field theory in dd dimensions with interaction ϕn\phi^n. A 1PI Feynman diagram has VV vertices, PP propagators, and EE external lines. Using Euler's relation L=P−V+1L = P - V + 1 for the number of loops, derive the superficial degree of divergence DD in terms of dd, nn, and EE.

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