Here the integration domain is over k restricted to a cube of side length ⁠ 2π / a ⁠, so that large values of k are not allowed. It is important to note that the k -measure contains the factors of 2 π from Fourier transforms, this is the best standard convention for k -integrals in QFT. The lattice means that fluctuations at large k are not allowed to contribute right away, they only start to contribute in the limit a → 0. Sometimes, instead of a lattice, the field modes are just cut off at high values of k instead.