Communications in Mathematical Physics

, Volume 346, Issue 3, pp 1021–1050

Characterization of Reflection Positivity: Majoranas and Spins


DOI: 10.1007/s00220-015-2545-z

Cite this article as:
Jaffe, A. & Janssens, B. Commun. Math. Phys. (2016) 346: 1021. doi:10.1007/s00220-015-2545-z


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.

Funding information

Funder NameGrant NumberFunding Note
Templeton Religion Trust
    • Grant 613.001.214

    Copyright information

    © Springer-Verlag Berlin Heidelberg 2016

    Authors and Affiliations

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

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