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Czechoslovak Journal of Physics

On convenient parametrization of boundary conditions for some models of quantum mechanics

E. Kapuścik, Agnieszka Kijanka-Dec, J. Podlaska

Published Nov 1, 2005• 1 citation
Publisher
DOI
10.1007/s10582-006-0023-8

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The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange formalism preserves relativistic covariance which makes the Feynman method very convenient to achieve the renormalization of field theories both in perturbative and non-perturbative approaches. However, when the systems are confined in bounded domains we shall show that the path integral approach does not describe the most general type of boundary conditions. Highly non-local boundary conditions cannot be described by Feynman's approach. We analyse in this note the origin of this problem in quantum mechanics and its implications for field theory.
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Spontaneous parametric down-conversion is a convenient source of pairs of entangled photons. Within special interferometric configurations involving either two sources of this kind or double emissions from such a source, one can observe three-photon Greenberger-Horne-Zeilenger--type interference effects. Unfortunately, events of some other types necessarily occur. It is shown that under specific operational conditions, thus far not met by the experiments, the entirety of the phenomena observed in such experiments has no local realistic model. However, one can show this only by analyzing the entire pattern of all events predicted by quantum mechanics.