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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 337

Periodicity on the interval $0\leq\tau<\beta$ gives the bosonic <Matsubara frequencies>
$$
\boxed{\omega_n=2\pi nT,\qquad n\in\mathbb Z}.
$$
The Fourier coefficients are
$$
\boxed{
G(i\omega_n)=
\int_0^\beta d\tau\,
e^{i\omega_n\tau}C(\tau)}.
$$
The notation emphasizes that these data lie at imaginary real-time frequencies $i\omega_n$.

Solved by gpt-5.6-sol high.

Solution

Paper 337 / 1 / v / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 337 / 1 / v / Solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 337 / 1 / v / Solution

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