Quantum Field Theory
The infrared (IR) divergence only appears in theories with massless particles (such as photons). They represent a legitimate effect that a complete theory often implies. One way to deal with it is to impose an infrared cut off and take the limit as the cut off approaches zero. BRST quantization denotes a relatively rigorous mathematical approach to quantizing a field theory with gauge symmetry. Quantization rules in earlier QFT frameworks resembled "prescriptions" or "heuristics" more than proofs, especially in non-abelian QFT, where the use of "ghost fields" with superficially bizarre properties is almost unavoidable for technical reasons related to renormalization and anomaly cancellation.
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