Plasma in a monopole background does not have a twisted Poisson structure

Manuel Lainz, Cristina Sardón, and Alan Weinstein
Phys. Rev. D 100, 105016 – Published 19 November 2019

Abstract

For a particle in the magnetic field of a cloud of monopoles, the naturally associated 2-form on phase space is not closed, and so the corresponding bracket operation on functions does not satisfy the Jacobi identity. Thus, it is not a Poisson bracket; however, it is twisted Poisson in the sense that the Jacobiator comes from a closed 3-form. The space D of densities on phase space is the state space of a plasma. The twisted Poisson bracket on phase-space functions gives rise to a bracket on functions on D. In the absence of monopoles, this is again a Poisson bracket. It has recently been shown by Heninger and Morrison that this bracket is not Poisson when monopoles are present. In this note, we give an example where it is not even twisted Poisson.

  • Received 19 August 2019

DOI:https://doi.org/10.1103/PhysRevD.100.105016

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Plasma PhysicsGeneral PhysicsParticles & Fields

Authors & Affiliations

Manuel Lainz* and Cristina Sardón

  • Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), calle Nicolás Cabrera, 13-15, Campus Cantoblanco, UAM 28049 Madrid, Spain

Alan Weinstein

  • Department of Mathematics, University of California, Berkeley, California 94720, USA

  • *manuel.lainz@icmat.es
  • cristinasardon@icmat.es
  • alanw@math.berkeley.edu

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Issue

Vol. 100, Iss. 10 — 15 November 2019

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