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


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.


Heisenberg Group Central Extension Poisson Structure Cohomology Theory Maxwell Theory 
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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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