Finally, I have found time to think about, and the incentive to study, how the
field theory of Topological thermodynamics, electrodynamics, and hydrodynamics
can be compared to field theory concepts that have been developed by Lagrangian
methods, for both the classic and quantum mechanical varieties. For more than
30 years I have known that Cartan's topological methods could be applied to
dissipative systems; the methods based on diffeomorphic-invariant Lagrangian
field theories can not. The incentive came when I realized that the topological
methods of Cartan gave dynamical results that can explain "symmetry breaking"
and quantization in terms of continuous topological evolution.
Category: Mathematical Physics