1201.5806 (E. A. Tagirov)
E. A. Tagirov
This is the second of the two related papers analysing origins and possible
explanations of a paradoxical phenomenon of the quantum potential (QP). It
arises in quantum mechanics'(QM) of a particle in the Riemannian
$n$-dimensional configurational space obtained by various procedures of
quantization of the non-relativistic natural Hamilton systems. Now, the two
questions are investigated: 1)Does QP appear in the non-relativistic QM
generated by the quantum theory of scalar field (QFT) non-minimally coupled to
the space-time metric? 2)To which extent is it in accord with quantization of
the natural systems? To this end, the asymptotic non-relativistic equation for
the particle-interpretable wave functions and operators of canonical
observables are obtained from the primary QFT objects. It is shown that, in the
globally-static space-time, the Hamilton operators coincide at the origin of
the quasi-Euclidean space coordinates in the both altenative approaches for any
constant of non-minimality $\tilde\xi$, but a certain requirement of the
Principle of Equivalence to the quantum field propagator distinguishes the
unique value $\tilde\xi = 1/6$. Just the same value had the constant $\xi$ in
quantum Hamiltonians arise from the traditional quantizations of the natural
systems: the DeWitt canonical, Pauli-DeWitt quasiclassical, geometrical and
Feynman ones, as well as in the revised Schr\"{o}dinger variational
quantization. Thus, QP generated by mechanics is tightly related to
non-minimality of the quantum scalar field. Meanwhile, an essential discrepancy
exists between the non-relativistic QMs derived from the two altenative
approaches: QFT generate a scalar QP, whereas various quantizations of natural
mechanics, lead to PQs depending on choice of space coordinates as physical
observables and non-vanishing even in the flat space if the coordinates are
curvilinear.
View original:
http://arxiv.org/abs/1201.5806
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