Communications in Mathematical Physics

, Volume 155, Issue 1, pp 27–46 | Cite as

Optimal hypercontractivity for fermi fields and related non-commutative integration inequalities

  • Eric A. Carlen
  • Elliott H. Lieb
Article
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Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

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

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