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arXiv · 1204.1361

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

Zhi-Qiang Guo·Ivan Schmidt
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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.

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Zhi-Qiang Guo, Ivan Schmidt. 2012-08-03. Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation. https://doi.org/10.1103/physrevd.86.045012

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