Abstract
We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant under "duality rotations" of the vector fields into one another. The commutators of the Hamiltonian and momentum densities are shown to be necessarily those of the Poincaré group or its zero signature contraction. Space-time structure thus emerges out of the principle of duality.
Highlights
We consider all possible dynamical theories which evolve two transverse vector fields out of a threedimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant under ‘‘duality rotations’’ of the vector fields into one another
In its most generic formulation, the principle of electric-magnetic duality states that the electric field density Ei and magnetic field density Bi are to be treated on the same footing
Gives the following precise meaning to the expression ‘‘on the same footing:’’ one demands rotational invariance in the two-dimensional plane whose axes are labeled by the index a. These rotations are termed ‘‘duality rotations.’’ If one demands that the Bia should have a dynamical evolution with a Hamiltonian structure, one needs to introduce a Poisson bracket among them
Summary
We consider all possible dynamical theories which evolve two transverse vector fields out of a threedimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant under ‘‘duality rotations’’ of the vector fields into one another. These rotations are termed ‘‘duality rotations.’’ If one demands that the Bia should have a dynamical evolution with a Hamiltonian structure, one needs to introduce a Poisson bracket among them. The simplest possibility that is invariant under duality rotations and spatial rotations, is local in space, and is consistent with the divergence-free character, B
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