The Uncertainty of Fluxes

Details The Uncertainty of Fluxes The Uncertainty of Fluxes

2006-05-19

arxiv.org/abs/hep-th/0605198v3

Commun.Math.Phys.271:247-274,2007

Physics

High Energy Physics

High Energy Physics - Theory

33 pages; minor modifications for publication in Commun. Math. Phys

Scientific paper

10.1007/s00220-006-0181-3

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/2-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.

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