We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all “experimental propositions” of M and we look for a model of quantum logic in relati...We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all “experimental propositions” of M and we look for a model of quantum logic in relation to the quantization of the base manifold M. In particular we give a new interpretation about previous results of the author in order to build an “asymptotics quantum probability space” for the Hilbert lattice L(H).展开更多
We show how the metric of a five-dimensional hyperspace-time can be used to model the quantum nature of electromagnetic interactions. The space-time neighborhood of the point where such an interaction takes place bend...We show how the metric of a five-dimensional hyperspace-time can be used to model the quantum nature of electromagnetic interactions. The space-time neighborhood of the point where such an interaction takes place bends according to the curl and the derivative of the local electromagnetic four-potential, both calculated in the direction of the latter. In this geometric setting, the presence of a non-gravitational field is needed to induce the discretization of any gravitational field. We also exploit two variants of the classical Kaluza-Klein five-dimensional theory to obtain coupled generalizations of Einstein’s and Maxwell’s equations. The first variant involves an unspecified scalar field that may be related to the inflaton. The equations of the second variant show a direct interdependency of gravitation and electromagnetism that would emerge or be activated through the production of electromagnetic waves.展开更多
This article presents a mathematical framework for group-theoretical formalism of quan-tum mechanics and discusses the geometric quantization of the classical systems associatedwith a Lie group. The classical-quantum ...This article presents a mathematical framework for group-theoretical formalism of quan-tum mechanics and discusses the geometric quantization of the classical systems associatedwith a Lie group. The classical-quantum correspondence is realized by identifying quantumobservable algebra and its classical analogue with the set of distributions with compact sup-ports OD a Lie group and on the associated Lie algebra respectively, both having a convolu-tion-type associative algebraic structure. The general mathematical constructs are illustratedby studying systems associated with the Heisenberg-Weyl group. It is shown that the expo-nential mapping from Heisenberg-Weyl algebra to the corresponding Lie group gives Weyl quan-tization.展开更多
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism and improvements on the sophisticated theory of geometric quantization are presented touching brief...A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the “salient points of the theory”. The unfamiliar reader can consider this as a “soft” introduction to the topic.展开更多
We review the themes relating to the proposition that“quantization commutes with reduction”([Q,R]=0),from symplectic manifolds to Cauchy-Riemann manifolds.
几何攻击会给数字水印带来同步误差和插值误差,现有的多数抗几何攻击的鲁棒水印方法都把焦点集中在同步误差上,对插值误差的研究甚少。介绍了常见的插值算法并指明了插值误差产生的原因,能够实现最佳的嵌入率、嵌入失真以及鲁棒性之间...几何攻击会给数字水印带来同步误差和插值误差,现有的多数抗几何攻击的鲁棒水印方法都把焦点集中在同步误差上,对插值误差的研究甚少。介绍了常见的插值算法并指明了插值误差产生的原因,能够实现最佳的嵌入率、嵌入失真以及鲁棒性之间平衡的QIM(quantization index modulation)水印算法,进而分析了插值误差对QIM算法的影响,在此基础上提出了针对插值误差的逐像素点选择QIM水印算法。实验在纹理程度不同的10幅图像上进行。实验证明,提出的水印算法对插值误差的鲁棒性优于原始的QIM水印算法。展开更多
文摘We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all “experimental propositions” of M and we look for a model of quantum logic in relation to the quantization of the base manifold M. In particular we give a new interpretation about previous results of the author in order to build an “asymptotics quantum probability space” for the Hilbert lattice L(H).
文摘We show how the metric of a five-dimensional hyperspace-time can be used to model the quantum nature of electromagnetic interactions. The space-time neighborhood of the point where such an interaction takes place bends according to the curl and the derivative of the local electromagnetic four-potential, both calculated in the direction of the latter. In this geometric setting, the presence of a non-gravitational field is needed to induce the discretization of any gravitational field. We also exploit two variants of the classical Kaluza-Klein five-dimensional theory to obtain coupled generalizations of Einstein’s and Maxwell’s equations. The first variant involves an unspecified scalar field that may be related to the inflaton. The equations of the second variant show a direct interdependency of gravitation and electromagnetism that would emerge or be activated through the production of electromagnetic waves.
文摘This article presents a mathematical framework for group-theoretical formalism of quan-tum mechanics and discusses the geometric quantization of the classical systems associatedwith a Lie group. The classical-quantum correspondence is realized by identifying quantumobservable algebra and its classical analogue with the set of distributions with compact sup-ports OD a Lie group and on the associated Lie algebra respectively, both having a convolu-tion-type associative algebraic structure. The general mathematical constructs are illustratedby studying systems associated with the Heisenberg-Weyl group. It is shown that the expo-nential mapping from Heisenberg-Weyl algebra to the corresponding Lie group gives Weyl quan-tization.
文摘A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the “salient points of the theory”. The unfamiliar reader can consider this as a “soft” introduction to the topic.
文摘We review the themes relating to the proposition that“quantization commutes with reduction”([Q,R]=0),from symplectic manifolds to Cauchy-Riemann manifolds.
文摘几何攻击会给数字水印带来同步误差和插值误差,现有的多数抗几何攻击的鲁棒水印方法都把焦点集中在同步误差上,对插值误差的研究甚少。介绍了常见的插值算法并指明了插值误差产生的原因,能够实现最佳的嵌入率、嵌入失真以及鲁棒性之间平衡的QIM(quantization index modulation)水印算法,进而分析了插值误差对QIM算法的影响,在此基础上提出了针对插值误差的逐像素点选择QIM水印算法。实验在纹理程度不同的10幅图像上进行。实验证明,提出的水印算法对插值误差的鲁棒性优于原始的QIM水印算法。
