Renormalization and Loop Momentum Flow

Tree versus loop structure, ultraviolet sensitivity, and bare-to-measured parameters.

Exercise 1

Why loops are different

Intermediateloopstree levelmomentum flow

Explain the qualitative difference between a tree diagram and a loop diagram in perturbation theory.

Subparts

Why are tree-level internal momenta fixed by external data?

Why does a loop introduce a momentum integral?

Exercise 2

Advancedultravioletdivergencepower counting

Describe in words how large loop momentum can lead to divergent behavior.

Subparts

What part of the loop integral is dangerous?

Why does the answer depend on the theory and dimension?

Exercise 3

Advancedbare parametersrunning couplingrenormalization group

What does it mean to say that a measured coupling is obtained from a bare parameter plus quantum corrections?

Subparts

Write the idea schematically.

Explain why the measured quantity can depend on scale.

Next sheet

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