The theoretical description of fermionic system with strong interaction is a very challenging open problem in physics. The most notable (but far from the only) experimental realization of this... Show moreThe theoretical description of fermionic system with strong interaction is a very challenging open problem in physics. The most notable (but far from the only) experimental realization of this type of systems are the cuprate superconductors which have zero electric resistivity. Even if onehas a good microscopic model for the description of these materials it is very hard to translate it to macroscopic observables which in principle can be experimentally checked. The problem is that in case of a relevant interaction one can not Taylor expand in the coupling constant in the low-energy regime in which we are most interested. On the other hand, because of the fermion sign problem Monte Carlo numerical techniques (which are succesful with bosonic models) do not work for fermions at finite density. This thesis is devoted to the applications of several methods to the research area described above. The common theme of these techniques is that they are (partly) motivated from high-energy physics: the research area which deals with particle physics, string theory etc. Show less
