The Significance of Generalized Gauge Transformation across Fundamental Interactions

The author of this paper has put forward a unified program of gauge field from the mathematical and physical picture of the principal associated bundles: thinking that our universe may have more fundamental interactions than the four fundamental interactions, and these basic interaction gauge fields are only the projection components to the base manifold, that is our universe, from a unified gauge potential or connection of the principal associated bundle manifold on the base manifold. These components can satisfy the transformation of gauge potential, and can even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, that is, the generalized gauge Equation (GGE), but the gauge potential or connection on the principal bundle is invariant, corresponding to the invariance of gauge transformation [1]. In this paper, we will continue to discuss this aspect concretely, and specifically construct a spatiotemporal model with the frame bundle as the principal bundle, and the tensor bundle as the associated bundle, so that the four fundamental interactions, especially the electromagnetic interaction and the gravitational interaction, can be reflected in the bottom manifold, that is, the regional distributions in our universe. Furthermore, this paper studies the existence of gauge transformation across basic interactions by establishing a model of gauge transformation of basic interaction field;it is found that the unified expression formula is GGE and the expression relation on the curvature of space-time. Therefore, the author discusses the feasibility of the generalized gauge transformation across the basic electromagnetic interaction and the basic gravitational interaction, and on this basis, specifically determines a method or way to find the generalized gauge transformation, so as to try to realize the last step of the “unification” of the four fundamental interactions in physics, that is, the “unification” of electromagnetism and gravity.

An Outline of the Grand Unified Theory of Gauge Fields

This paper attempts to propose a grand unified guiding principle of gauge fields from the mathematical and physical picture of fiber bundles: it is believed that our universe may have more fundamental interactions than the four fundamental interactions, and the gauge fields of these fundamental interactions are just a unified gauge potential on the fiber bundle manifold or the components connected to the bottom manifold, that is, our universe;these components can meet the transformation of gauge potential, and even can be transformed from a fundamental interaction gauge potential to another fundamental interaction gauge potential, and can be summarized into a unified equation, namely the expression of the generalized gauge equation, corresponding to the gauge transformation invariance;so gauge transformation invariance is a necessary condition to unify field theory, but quantization of field is not a necessary condition;the four (or more) fundamental interaction fields of the universe are unified into a universal gauge field defined by the connection of the principal fiber bundle on the cosmic base manifold.

Characteristics of Coherence and Information for the Davydov Soliton Field

In this work, a generalized Davydov soliton field (DSF) has been investigated. The characteristics of correlation and information for the filed are emphasized and studied. It is a sort of correlation among so called generalized solitons so that the field may appear to some macroscopic quantum properties such as the superconductivity at room temperature. Secondly, the character of information for the field can be described by a nonlinear Liouville equation in the quantum information representation. This provides a basis to express information quality of DSF, which means that DSF can influence or drive object by using (soliton type of) quantum information density. All these two aspects provide a foundation which possibly explains many potential biological functions of human body such as some complex bio-electromagnetic phenomena and their interactions with objects.

Some Charicteristics and Applications for Quantum Information

In this work some charicteristics and applications for quantum information is revealed. The various dynamical equations of quantum information density have been investigated, transmission characteristics of the dynamical mutual information have been studied, and the decoherence-free controlling procedure has been considered, which exposes that quantum information is holographic through the similarity structure of subdynamic kinetic equations for quantum information density.

Oscillation of Davydov Solitons in Three Wells

In this work, we propose a model of oscillation of Davydov solitons in three wells. It can be used as a mathematical and physical frame in simulation of circle of some nonlinear oscillation of excitations via acupuncture system. The calculation shows that this sort of oscillation is possible if the initial rate of average occupational number of the quasi-particles in the wells is not equal to zero. One of oscillations arising relies on the initial rate of average occupational number of quasi-particles to be equal with each other within three wells. Then, the oscillation is not a kind of Josephson oscillation and has complicated frequency distributions. However, the total behavior of oscillation played is similar to three big solitons concentrated in three wells. In this sense, this model generally reveals a sort of oscillation mechanism of the acupuncture system how to work in the body, which allows us to understand the oscillation that may be one of fundamental natures in the acupuncture system.

Nonlinear Liouville Equation and Information Soliton

In this work, some types of nonlinear Liouville equation (NLE) and nonlinear Master equations (NME) are studied. We found that the nonlinear terms in the equation can resist state of system damping so that an information solitonic structure appears. Furthermore, the power in the non-linear term is independent of limitation of the solution. This characteristic offers a possibility to construct complicated information solitons from some simple solutions, which allow one to solve complicated NLE or NME. The results obtained in this work may provide an innovated channel for the quantum information transmission over far distance against dissipation and decoherence, and also open a constructive way to resist age decaying of system by designing adjusted field interaction with the system nonlinearly.

Fluctuation of Quantum Information Density in Curved Time-Space

A dynamical equation for quantum information density （QID） in curved spacetime is presented. The related fluctuation of QID with quantum Einstein equation is also discussed, which reveals the measuring of the dynamical mutual information condition using a Gaussian quantum channel.

A harmonious unifying hybrid preferential model and its universal properties for complex dynamical networks

To describe the real world which is a harmonious unification world with both de- terminism and randomness, we propose a harmonious unifying hybrid preferential model (HUHPM) of a certain class of complex dynamical networks. HUHPM is gov- erned only by the total hybrid ratio d/r according to the practical need. As some typical examples, the concepts and methods of the HUHPM are applied to the un-weighted BA model proposed by Barabási et al., the weighted BBV model pro- posed by Barat et al. and the weighted TDE model proposed by Wang et al. to get the so-called HUHPM-BA network, HUHPM-BBV network and HUHPM-TDE network. These HUHPM networks are investigated both analytically and numerically. It is found that the HUHPM reveals several universal properties, which more approach to the real-world networks for both un-weighted and weighted networks and have potential for applications.