Unfinished History and Paradoxes of Quantum Potential. II. Relativistic Point of View

Details Unfinished History and Paradoxes of Quantum Potential. II. Relativistic Point of View Unfinished History and Paradoxes of Quantum Potential. II. Relativistic Point of View

2012-01-27

arxiv.org/abs/1201.5806v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, based on the plenary talk at the A. Z. Petrov Centenary Memorial International Symposium, 1-7.11.2010, Kazan, Russia

Scientific paper

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 the quantum Hamiltonians arising 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.

Affiliated with

Also associated with

No associations

Rating

Unfinished History and Paradoxes of Quantum Potential. II. Relativistic Point of View does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Unfinished History and Paradoxes of Quantum Potential. II. Relativistic Point of View, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unfinished History and Paradoxes of Quantum Potential. II. Relativistic Point of View will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-345145