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The fermion sign problem is studied in the path integral formalism. Thestandard picture of Fermi liquids is first critically analyzed, pointing outsome of its rather peculiar properties. The insightful work of Ceperley inconstructing fermionic path integrals in terms of constrained world-lines isthen reviewed. In this representation, the minus signs associated withFermi-Dirac statistics are self consistently translated into a geometricalconstraint structure (the {\em nodal hypersurface}) acting on an effectivebosonic dynamics. As an illustrative example we use this formalism to study1+1-dimensional systems, where statistics are irrelevant, and hence the signproblem can be circumvented. In this low-dimensional example, the structure ofthe nodal constraints leads to a lucid picture of the entropic interactionessential to one-dimensional physics. Working with the path integral inmomentum space, we then show that the Fermi gas can be understood by analogy toa Mott insulator in a harmonic trap. Going back to real space, we discuss thetopological properties of the nodal cells, and suggest a new holographicconjecture relating Fermi liquids in higher dimensions to soft-core bosons inone dimension. We also discuss some possible connections between mixedBose/Fermi systems and supersymmetry.

Pacifying the Fermi-liquid: battling the devious fermion signs