Correlated Lattice Fermions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mi>∞</mml:mi></mml:math>Dimensions

We show that even in $d=\ensuremath{\infty}$ dimensions the Hubbard model, when scaled properly, describes nontrivial correlations among fermions. Diagrammatic treatments are found to be substantially simpler than in finite dimensions. The weak-coupling correlation energy is seen to be a good approximation for that in $d=3$. Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in $d=\ensuremath{\infty}$.