The Uncertainty of Fluxes

• DOI: 10.1007/s00220-006-0181-3
• Publication Date: 2007-02-02T17:54:22Z
• Authors: Daniel S. Freed; Gregory W. Moore; Graeme Segal
• Keywords: Manifold (fluid mechanics)

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.<br/>33 pages; minor modifications for publication in Commun. Math. Phys<br/>