Matsubara summation
In thermal quantum field theory, the Matsubara summation (named after Takeo Matsubara) is a technique used to simplify calculations involving Euclidean (imaginary time) path integrals. In thermal quantum field theory, bosonic and fermionic quantum fields ϕ ( τ ) {\displaystyle \phi (\tau )} are respectively periodic or antiperiodic in imaginary time τ {\displaystyle \tau } , with periodicity β = ℏ / k B T {\displaystyle \beta =\hbar /k_{\rm {B}}T} .