The Uncertainty of Fluxes
Abstract
In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3manifold, 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 selfdual fields, noting that they are quantized by Pontrjagin selfdual cohomology theories and that the quantum Hilbert space is {mathbb{Z}/2mathbb{Z}} graded, so typically contains both bosonic and fermionic states. Significantly, these ideas apply to the RamondRamond field in string theory, showing that its Ktheory class cannot be measured.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 April 2007
 DOI:
 10.1007/s0022000601813
 arXiv:
 arXiv:hepth/0605198
 Bibcode:
 2007CMaPh.271..247F
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Algebraic Topology;
 Mathematics  Mathematical Physics
 EPrint:
 33 pages