Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

@article{29878,
   author = {Cremaschini, Claudio and Tessarotto, Massimo},
   article_number = {7},
   doi = {http://dx.doi.org/10.3390/e19070339},
   keywords = {covariant quantum gravity; Hamilton-Jacobi quantization; quantum-wave equation; quantum hydrodynamic equations; Heisenberg inequalities},
   language = {eng},
   issn = {1099-4300},
   journal = {Entropy},
   title = {Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity},
   url = {http://www.mdpi.com/1099-4300/19/7/339},
   volume = {19},
   year = {2017}
}

TY  - JOUR
ID  - 29878
AU  - Cremaschini, Claudio - Tessarotto, Massimo
PY  - 2017
TI  - Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity
JF  - Entropy
VL  - 19
IS  - 7
SP  - „339-1“-„339-20“
EP  - „339-1“-„339-20“
SN  - 10994300
KW  - covariant quantum gravity
KW  - Hamilton-Jacobi quantization
KW  - quantum-wave equation
KW  - quantum hydrodynamic equations
KW  - Heisenberg inequalities
UR  - http://www.mdpi.com/1099-4300/19/7/339
L2  - http://www.mdpi.com/1099-4300/19/7/339
N2  - Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015-2017) are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG) wave equation, which advances the quantum state psi associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton-Jacobi quantization of the classical variational tensor field g equivalent to {g_(mu nu)} and its conjugate momentum, referred to as (canonical) g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for psi, which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state y is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g equivalent to {g_(mu nu)} and its quantum conjugate momentum operator.
ER  - 

CREMASCHINI, Claudio a Massimo TESSAROTTO. Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity. \textit{Entropy}. 2017, roč.~19, č.~7, s.~„339-1“-„339-20“, 20 s. ISSN~1099-4300. Dostupné z: https://dx.doi.org/10.3390/e19070339.