= Matsubara frequency
{c}
{wiki}
<Matsubara frequencies> are the discrete Fourier frequencies on an <imaginary time> thermal interval. With $\hbar=k_B=1$ and $\beta=1/T$, periodic <bosonic> fields have $\omega_n=2\pi nT$, while antiperiodic <fermionic> fields have $\omega_n=(2n+1)\pi T$.
Their difference follows from requiring the Fourier phase to return with the appropriate sign after one thermal period. The <bosonic> zero mode can dominate long-distance finite-temperature fluctuations, whereas <fermions> have no zero Matsubara mode in the ordinary thermal trace. These are labels in an <imaginary time> calculation, not discrete frequencies of an externally applied real-time drive. Extracting a real-frequency response requires the corresponding analytic continuation and spectral information.
Back to article page
