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Quantum motion on a torus as a submanifold problem in a generalized Dirac's theory of second-class constraints | | D. M. Xun
; Q. H. Liu
; X. M. Zhu
; | | Date: |
27 Dec 2012 | | Abstract: | The present formalism of Dirac’s theory for a system of second-class
constraints can be well formulated either within purely intrinsic geometric
framework or beyond, but whatever framework is taken, the results are not well
compatible with those given by the Schr"odinger’s theory. A generalization of
the Dirac’s theory is made recently (Phys. Rev. A 84, 042101(2011)) to include
the commutation relations [f,H], where f= position x_{i}, momentum p_{i} and
Hamiltonian H, into the formalism as the second category of the fundamental
ones. Through a careful analysis of the quantum motion on a torus, we
demonstrate that the purely intrinsic geometry does not suffice for the Dirac’s
theory to be self-consistent, but an extrinsic examination of the torus in
three dimensional flat space does. Thus the Dirac’s theory turns out to be
complementary to the Schr"odinger’s one. The former eliminates the intrinsic
description, and the latter gives the unique form of the geometric potential,
while both define the identical form of the geometric momentum. | | Source: | arXiv, 1212.6373 | | Services: | Forum | Review | PDF | Favorites | |
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