| The fermion sign problem, i.e. the fact that it is impossible to address problems of infinities of interacting fermions with controlled mathematical methods, seems at the core of the present intellectual crisis in condensed matter physics. The empirical fruitfly is embodied by the fermionic quantum critical states found in heavy fermion systems and possibly also in the metallic state of the high Tc superconductors. Resting on an alternative 'constrained' path integral formalism due to Ceperley it appears that we have discovered an alternative framework that at the least gives very new insights in fermion systems that are scale invariant. In this language Fermi-Dirac statistics turns into the classification of geometries of nodal hypersurfaces and we discovered an explicit example where this surface into a fractal, reproducing in turn essential features of the heavy fermion quantum critical state. |
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