Article

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

04/2012; DOI:10.1103/PhysRevD.86.045012
Source: arXiv

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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Keywords

classical theories
 
conventional Lagrangian
 
fermion field
 
field theories
 
first order Lagrangian
 
gauge field
 
lattice theories
 
mass term
 
massive term
 
nontrivial results
 
quantum theories
 
special solutions