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Conjugate variables in quantum field theory and a refinement of Pauli’s theorem

Steffen Pottel1,* and Klaus Sibold2,†

  • 1Max-Planck Institute for Mathematics in the Sciences, Inselstraße 22 D-04103 Leipzig, Germany
  • 2Institut für Theoretische Physik, Universität Leipzig, Postfach 100920 D-04009 Leipzig, Germany

  • *pottel@mis.mpg.de
  • †sibold@physik.uni-leipzig.de
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Phys. Rev. D 94, 065008 – Published 9 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.065008

Abstract

For the case of spin zero, we construct conjugate pairs of operators on Fock space. On states multiplied by polarization vectors, coordinate operators Q conjugate to the momentum operators P exist. In the massive case the notion of interest is derived from a geometrical quantity, the massless case is realized by taking the limit m2→0 on the one hand, on the other, starting with m2=0 directly, from conformal transformations. The norm problem of the states on which the Q’s act is crucial: the states determine eventually how many independent conjugate pairs exist. It is intriguing that (light-) wedge variables and, hence, the wedge-local case seem to be preferred.

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See Also

Preconjugate variables in quantum field theory and their applications

Albert Much, Steffen Pottel, and Klaus Sibold
Phys. Rev. D 94, 065007 (2016)

Article Text

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Phys. Rev. D 94, 065008– Published 9 September, 2016
  • Received 1 June 2016

© 2016 American Physical Society

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