Inequalities pp 151-170 | Cite as

Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration Inequalities

  • Eric A. Carlen
  • Elliott H. Lieb


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.


Conditional Expectation Clifford Algebra Dirichlet Form Logarithmic Sobolev Inequality Full Matrix Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Eric A. Carlen
    • 2
  • Elliott H. Lieb
    • 1
  1. 1.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

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