Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 4 / b

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- Solution b

Solution

With all momenta incoming, the Feynman rules are

propagator: \frac{i}{p ^{2} - m ^{2} + i ϵ},

(1)

three-point vertex: 2 iλ \sum_{j = 1}^{3} (p_{j}^{2} - m^{2}),

(2)

and

four-point vertex: 4 i λ^{2} (\sum_{j = 1}^{4} p_{j}^{2} - 3 m^{2}) .

(3)

Each vertex includes its momentum-conserving delta function. The combinatorial factors follow by assigning the identical fields to the differentiated and undifferentiated slots in every possible way.

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Paper 301
iii
2025
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
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Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 4 / b

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