Monday, June 18, 2012

1206.3301 (Christian Lessig et al.)

The Geometry of Radiative Transfer    [PDF]

Christian Lessig, Alex L. Castro, Eugene Fiume
We present the geometric structure of radiative transfer and the symmetries associated with its known conserved quantities. Our geometrization exploits recent work in the literature that enables the Hamiltonian formulation of radiative transfer to be obtained from a phase space representation of electromagnetic theory. Cosphere bundle reduction yields the traditional description over the space of "positions and directions", and geometrical optics arises as a special case when energy is disregarded. It is also shown that, in idealized environments, radiative transfer is a Lie-Poisson system with the group of canonical transformations as configuration space and symmetry group.
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