> Though I have read that some equatins regarding sub atomic particles were "too difficult to solve" before, I never had read a good explanation why.
Solution to the equations of quantum field theory can be formally expressed using what's called a perturbation expansion. This is similar to using a power series expansion to solve an algebraic or differential equation. In a rough way of looking at things, higher order terms in the expansion correspond to particle interactions with more "stuff" involved. This equivalence is what Feynman diagrams represent.
In the case of electromagnetism, this technique is very effective. The term corresponding to a single photon exchange is 137 times larger than the term corresponding to two photons, and so on. As a result, perturbation theory works very well for these calculations.
However, for nuclear forces in a proton or neutron, all the terms are about the same size. You can't cut off the expansion and get a meaningful estimate. In the Feynman diagram view, this is saying that you can't think of it as just exchanges of small numbers of gluons, rather, you'd need to consider huge number of particles and diagrams of extreme complexity. This is the sense in which the equations are "too difficult to solve". You need to do something totally different from perturbation theory to get a solution. Lattice computations, as described in the article, are the best alternative technique we have available at this point.
Solution to the equations of quantum field theory can be formally expressed using what's called a perturbation expansion. This is similar to using a power series expansion to solve an algebraic or differential equation. In a rough way of looking at things, higher order terms in the expansion correspond to particle interactions with more "stuff" involved. This equivalence is what Feynman diagrams represent.
In the case of electromagnetism, this technique is very effective. The term corresponding to a single photon exchange is 137 times larger than the term corresponding to two photons, and so on. As a result, perturbation theory works very well for these calculations.
However, for nuclear forces in a proton or neutron, all the terms are about the same size. You can't cut off the expansion and get a meaningful estimate. In the Feynman diagram view, this is saying that you can't think of it as just exchanges of small numbers of gluons, rather, you'd need to consider huge number of particles and diagrams of extreme complexity. This is the sense in which the equations are "too difficult to solve". You need to do something totally different from perturbation theory to get a solution. Lattice computations, as described in the article, are the best alternative technique we have available at this point.