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By employing special solutions of the Hamilton-Jacobi equation and tools fromlattice theories, we suggest an approach to convert classical theories toquantum theories for mechanics and field theories. Some nontrivial results areobtained for a gauge field and a fermion field. For a topologically massivegauge theory, we can obtain a first order Lagrangian with mass term. For thefermion field, in order to make our approach feasible, we supplement theconventional Lagrangian with a surface term. This surface term can also producethe massive term for the fermion.

Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation