# What’s lacking in our understanding of the strong interaction?

Most of the calculations in quantum mechanics are made using the perturbation calculus. That is, we assume that the theory with no interactions that describes a free particle is an approximation of the full theory, take the classical solution of the free equations, and then add corrections. There are usually infinitely many quantum corrections that need to be calculated, but they often form a series in which every next term is much smaller than the previous one, and calculating just few initial terms gives a good approximation of a full result.

The problem with strong interaction is that the interaction is so strong we cannot reasonably approximate the real physical states with free-particle states. That means we fail at the first step, and we cannot use the perturbation approach that works in other cases.

Anther problem with QCD is that gluon fields interact directly with itself, making even the classical equations are non-linear, as opposed to linear equations of QED (in which electromagnetic field does not interact directly with itself, but only with charged matter). And we don't have the right mathematical tools to fully solve non-linear equations. This is similar to Generla Relativity, which also has non-linear equations. Because of that in GR we only know very few exact solutions. QCD has the same problem, and because of that we need to relay more on the simulations than on analytical solutions.