Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration
Eric Carlen, Elliott Lieb
TL;DR
This paper establishes optimal hypercontractivity bounds for fermion oscillator semigroups, extending classical results to non-commutative settings and contributing new findings in non-commutative integration theory.
Contribution
It introduces the first optimal hypercontractivity bounds for fermion fields, paralleling Nelson's results for bosons, and develops new tools in non-commutative integration theory.
Findings
Derived optimal hypercontractivity bounds for fermion semigroups
Extended non-commutative integration techniques
Established foundational results for fermionic quantum systems
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. {}.
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