Online Wick's Theorem Calculator

Input expression: **[,,c(p)a(q)][-][,,c(r)a(s)]**

Latex code: **\delta_{q r}a^{\dagger}_{p}a_{s}-\delta_{p s}a^{\dagger}_{r}a_{q}**

Simplified expression:

Here I provide an online program for simplification of elementary operators using Wick's theorem. You may know that manually working out is rather awkward. You can input the expressions according to the following examples (Please excuse me for the ungly input grammars ...). Note that no spaces are allowed between the commas.

Sample input:

- Creation operator:
**[,,c(p)]**= - Annihilation operator:
**[,,a(p)]**= - Commutator:
**[,,c(p)a(p)][-][,,a(r)]**= - Anticommutator:
**[,,c(p)][+][,,a(q)]**= - Parentheses:
**([,,a(m)][-][,,c(p)a(q)])[-][,,c(r)a(s)]**= - Addition and substraction:
**[2/1,,a(m)]+[3/4,,a(m)]-[5/1,,a(m)]**= - Integrals:
**[1/1,h_pq,c(p)a(q)]+[1/2,g_pqrs,c(p)c(r)a(s)a(q)]**=