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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics