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Communications in Mathematical Physics

, Volume 271, Issue 1, pp 247–274 | Cite as

The Uncertainty of Fluxes

  • Daniel S. FreedEmail author
  • Gregory W. Moore
  • Graeme Segal
Article

Abstract

In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3-manifold, we observe that magnetic and electric fluxes cannot be simultaneously measured. This uncertainty principle reflects torsion: fluxes modulo torsion can be simultaneously measured. We also develop the Hamilton theory of self-dual fields, noting that they are quantized by Pontrjagin self-dual cohomology theories and that the quantum Hilbert space is \({\mathbb{Z}/2\mathbb{Z}}\) -graded, so typically contains both bosonic and fermionic states. Significantly, these ideas apply to the Ramond-Ramond field in string theory, showing that its K-theory class cannot be measured.

Keywords

Heisenberg Group Central Extension Poisson Structure Cohomology Theory Maxwell Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Daniel S. Freed
    • 1
    Email author
  • Gregory W. Moore
    • 2
  • Graeme Segal
    • 3
  1. 1.Department of MathematicsUniversity of TexasAustinUSA
  2. 2.Department of PhysicsRutgers UniversityPiscatawayUSA
  3. 3.All Souls CollegeOxfordUnited Kingdom

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