An amplitude is ultraviolet finite if its regulated high-loop momentum contribution has a finite regulator-removal limit after whatever lower-order subtractions are specified. A zero superficial degree of divergence does not force divergence: gauge invariance can cancel the candidate local term. Conversely, superficial convergence alone does not exclude divergent subgraphs. Ultraviolet finiteness makes no claim about infrared divergences or physical threshold singularities.

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  1. Ultraviolet divergence
  2. Regularization in quantum field theory
  3. Renormalization
  4. Perturbative quantum field theory
  5. Quantum field theory
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