Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation
arXiv:1204.1361 · doi:10.1103/PhysRevD.86.045012
Abstract
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained for a gauge field and a fermion field. For a topologically massive gauge theory, we can obtain a first order Lagrangian with mass term. For the fermion field, in order to make our approach feasible, we supplement the conventional Lagrangian with a surface term. This surface term can also produce the massive term for the fermion.
arXiv comment30 pages, no figures, v2: discussions and references added, published version matched
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