Communications in Mathematical Physics

, Volume 346, Issue 3, pp 1021–1050 | Cite as

Characterization of Reflection Positivity: Majoranas and Spins

  • Arthur Jaffe
  • Bas Janssens


We study linear functionals on a Clifford algebra (algebra of Majoranas) equipped with a reflection automorphism. For Hamiltonians that are functions of Majoranas or of spins, we find necessary and sufficient conditions on the coupling constants for reflection positivity to hold. One can easily check these conditions in concrete models. We illustrate this by discussing a number of spin systems with nearest-neighbor and long-range interactions.


Gauge Transformation Gibbs State Global Gauge Twisted Product Global Gauge Transformation 
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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Harvard UniversityCambridgeUSA
  2. 2.Universiteit UtrechtUtrechtThe Netherlands

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