scholarly journals Fourier duality as a quantization principle

1997 ◽  
Vol 36 (2) ◽  
pp. 345-383
Author(s):  
R. Aldrovandi ◽  
L. A. Saeger
Keyword(s):  
Quantization Principle

Adaptive Semi-Fragile Watermarking Based on Complete Quantization and Image Contents

2013 ◽  
Vol 347-350 ◽  
pp. 2983-2988 ◽  
Author(s):  
Guo Wu ◽  
Da Wei Wei ◽  
Guang Ming Tang ◽  
Jin Feng Yang
Keyword(s):  
Low Frequency ◽  
Fragile Watermarking ◽  
Just Noticeable Difference ◽  
Wavelet Domain ◽  
Quantization Principle

Complete quantization principle is proposed in this paper, based on which, an adaptive semi-fragile watermarking algorithm based on image contents is proposed. The algorithm uses the low frequency sub-band to construct watermarking related to the content of image, and then uses just noticeable difference of wavelet domain to embed watermarking by means of complete quantitative principle. Experiments show this algorithm can classify malicious and non-malicious manipulations accurately.

scholarly journals Quaternionic quantization principle in general relativity and supergravity

2016 ◽  
Vol 31 (04n05) ◽  
pp. 1650004
Author(s):  
Martin Kober
Keyword(s):  
Field Theory ◽  
Plane Waves ◽  
Quantum Field ◽  
Commutation Relations ◽  
Algebraic Properties ◽  
Dirac Brackets ◽  
Canonical Quantum Gravity ◽  
Quantum Geometrodynamics ◽  
Canonical Quantum ◽  
Quantization Principle

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space–time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to [Formula: see text] supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.

scholarly journals GENERALIZED QUANTIZATION PRINCIPLE IN CANONICAL QUANTUM GRAVITY AND APPLICATION TO QUANTUM COSMOLOGY

2012 ◽  
Vol 27 (20) ◽  
pp. 1250106 ◽  
Author(s):  
MARTIN KOBER
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Dynamical Behavior ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Polynomial Method ◽  
Canonical Approach ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum ◽  
Quantization Principle

In this paper, a generalized quantization principle for the gravitational field in canonical quantum gravity, especially with respect to quantum geometrodynamics is considered. This assumption can be interpreted as a transfer from the generalized uncertainty principle in quantum mechanics, which is postulated as generalization of the Heisenberg algebra to introduce a minimal length, to a corresponding quantization principle concerning the quantities of quantum gravity. According to this presupposition there have to be given generalized representations of the operators referring to the observables in the canonical approach of a quantum description of general relativity. This also leads to generalized constraints for the states and thus to a generalized Wheeler–DeWitt equation determining a new dynamical behavior. As a special manifestation of this modified canonical theory of quantum gravity, quantum cosmology is explored. The generalized cosmological Wheeler–DeWitt equation corresponding to the application of the generalized quantization principle to the cosmological degree of freedom is solved by using Sommerfelds polynomial method.

The Schrödinger equation as the main quantization principle

Physica B+C ◽  
1988 ◽  
Vol 151 (1-2) ◽  
pp. 306-308
Author(s):  
E.E. Entralgo ◽  
V.V. Kuryshkin
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Quantization Principle
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