The Uncertainty of Fluxes
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 -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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- April 2007
- DOI:
- 10.1007/s00220-006-0181-3
- arXiv:
- arXiv:hep-th/0605198
- Bibcode:
- 2007CMaPh.271..247F
- Keywords:
-
- Heisenberg Group;
- Central Extension;
- Poisson Structure;
- Cohomology Theory;
- Maxwell Theory;
- High Energy Physics - Theory;
- Mathematical Physics;
- Mathematics - Algebraic Topology;
- Mathematics - Mathematical Physics
- E-Print:
- 33 pages