The uncertainty of fluxes

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 develo...

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Bibliographic Details
Published in:Communications in mathematical physics 2007-04, Vol.271 (1), p.247-274
Main Authors: FREED, Daniel S, MOORE, Gregory W, SEGAL, Graeme
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Classical electromagnetism, maxwell equations
Classical field theories
Electric flux
Electromagnetic fields
Exact sciences and technology
Functional analysis
General theory of fields and particles
Global analysis, analysis on manifolds
Hilbert space
Homology
Mathematical analysis
Mathematics
Physics
Sciences and techniques of general use
String theory
The physics of elementary particles and fields
Theory of fundamental strings
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Uncertainty principles
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-006-0181-3