Reflection positive doubles

Arthur Jaffe, Bas Janssens

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in nature. Within the framework of reflection positive doubles, we give necessary and sufficient conditions for reflection positivity. We use a reflection-invariant cone to implement our construction. Our characterization allows for a direct interpretation in terms of coupling constants, making it easy to check in concrete situations. We illustrate our methods with numerous examples.
Original languageEnglish
Pages (from-to)3506 - 3557
Number of pages52
JournalJournal of Functional Analysis
Issue number8
Publication statusPublished - 1 Apr 2017
Externally publishedYes


  • Reflection positivity
  • Tomita–Takesaki theory
  • Parafermions
  • Lattice gauge theory

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