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Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 306 / 3 / ii

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2024 iii Paper 306 3
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ii
Normal ordering defines a composite field by subtracting all singular self-contractions before bringing its constituent points together. For example,
:∂X∂X:(z)=limw→z​[∂X(z)∂X(w)−⟨∂X(z)∂X(w)⟩].
(1)
This makes T and Tˉ well-defined local operators and is equivalent in oscillator language to placing creation operators to the left of annihilation operators.

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