The uncertainty of fluxes

Daniel S. Freed, Gregory W. Moore, Graeme Segal

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

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 ℤ/2ℤ-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.

Original languageEnglish (US)
Pages (from-to)247-274
Number of pages28
JournalCommunications In Mathematical Physics
Volume271
Issue number1
DOIs
StatePublished - Apr 2007

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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