Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative   Integration
  Optimal hypercontractivity bounds for the fermion oscillator semigroup are obtained. These are the fermion analogs of the optimal hypercontractivity bounds for the boson oscillator semigroup obtained by Nelson. In the process, several results of independent interest in the theory of non-commutative integration are established. {}. 
Eric Carlen and Elliott Lieb