Chapter 26 g=0.06

Given the FT $$\tilde \phi(t,\vec p)=\sum e^{-i\vec p\cdot \vec x} \phi(t,\vec x)\\ \widetilde{\phi^3}(t,\vec p)=\sum e^{-i\vec p\cdot \vec x} \phi^3(t,\vec x)\\ $$ witht the lattice momentum $\vec p=2 \pi \vec n /L$, $\vec n \in \mathbb{Z}^3$ we define the correlators correlators: $$\langle\tilde\phi_0(t),\tilde\phi_0(0) \rangle\\ \langle\tilde\phi_0^3(t),\tilde\phi_0^3(0) \rangle\\ \langle \widetilde{\phi_0^3}(t)\widetilde{\phi_0^3}(0)\rangle\\ \langle\tilde\phi_1(t)\tilde\phi_1(0) \rangle\\ \frac{1}{9} \sum_{i,j}\langle\tilde\phi_0(t,0)\tilde\phi_0(t,p_j)\tilde\phi_0(t,-p_j)\tilde\phi_0(0,0) \tilde\phi_0(0,p_i),\tilde\phi_0(0,-p_i)\rangle\\ $$