Violation of Hudson's theorem in relativistic quantum mechanics

Andre G. Campos, Renan Cabrera, Denys I. Bondar, Herschel A. Rabitz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In nonrelativistic quantum mechanics, Hudson's theorem states that a Gaussian wave function is the only pure state corresponding to a positive Wigner function (WF). We explicitly construct non-Gaussian Dirac spinors with positive relativistic WFs. These pure relativistic states are coherent superpositions of particles and antiparticles, while the existence of positive WFs exclusive composed of particles is conjectured. These observations may open new directions in relativistic quantum information theory.

Original languageEnglish (US)
Article number034102
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
StatePublished - Sep 24 2014

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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