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arXiv · hep-th/0301052

On Hamiltonian formulations of the Schrödinger system

László Á. Gergely
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Abstract

We review and compare different variational formulations for the Schrödinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm yields the Schrödinger equation first as a consistency condition in the full phase space, second as canonical equation in the reduced phase space. The two methods lead to the same (reduced) Hamiltonian. As a third possibility, the Faddeev-Jackiw method is shown to be a shortcut of the Dirac method. By implementing the quantization scheme for systems with second class constraints, inconsistencies of previous treatments are eliminated.

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László Á. Gergely. 2003-01-09. On Hamiltonian formulations of the Schrödinger system. https://doi.org/10.1006/aphy.2002.6262

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