ADVANCES IN QUANTUM THEORY Edited by Ion I. Cotăescu Advances in Quantum Theory Edited by Ion I. Cotăescu Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2012 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. As for readers, this license allows users to download, copy and build upon published chapters even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Vana Persen Technical Editor Teodora Smiljanic Cover Designer InTech Design Team First published February, 2012 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Advances in Quantum Theory, Edited by Ion I. Cotăescu p. cm. ISBN 978-953-51-0087-4 Contents Preface IX Part 1 New Concepts in Quantum Theory 1 Chapter 1 Quantum Theory as Universal Theory of Structures – Essentially from Cosmos to Consciousness 3 T. Görnitz Chapter 2 Effects on Quantum Physics of the Local Availability of Mathematics and Space Time Dependent Scaling Factors for Number Systems 23 Paul Benioff Chapter 3 Quantum Theory of Multi-Local Particle 51 Takayuki Hori Part 2 Quantum Matter 75 Chapter 4 Quantum Theory of Coherence and Polarization of Light 77 Mayukh Lahiri Chapter 5 The Role of Quantum Dynamics in Covalent Bonding – A Comparison of the Thomas-Fermi and Hückel Models 107 Sture Nordholm and George B. Bacskay Chapter 6 Hydrogen Bonds and Stacking Interactions on the DNA Structure: A Topological View of Quantum Computing 153 Boaz Galdino de Oliveira and Regiane de Cássia Maritan Ugulino de Araújo Part 3 Quantum Gravity 173 Chapter 7 Quantum Fields on the de Sitter Expanding Universe 175 Ion I. Cotăescu VI Contents Chapter 8 The Equivalence Theorem in the Generalized Gravity of f(R)-Type and Canonical Quantization 203 Y. Ezawa and Y. Ohkuwa Chapter 9 Gravitational Quantisation and Dark Matter 221 Allan Ernest Preface The physics studies simple systems looking for fundamental interactions governing the dynamics of elementary constituents of the matter. The significance of these notions was evolving in the last three centuries from the concept of the force acting on macroscopic objects in the classical mechanics and electromagnetism up to the modern idea of the gauge fields intermediating the interactions among elementary particles. This is the historic way from the Newtonian mechanics to the actual quantum theory of fields. The quantum physics is born at the level of the atomic physics where the classical ideas of determinism and accuracy in physical experiments as well as the common intuition of the daily-life were inadequate for understanding the new phenomenology of the quantum world. The quantum systems can be measured only interacting with a macroscopic apparatus which is supposed to obey exactly the laws of the classical physics. This determine (or prepare) the measured state of the quantum system whose causal motion is stopped during the experiment. Moreover, the influence of the apparatus remains partially unknown such that some measured quantities are affected by uncertainty. Reversely, one cannot measure a quantum system evolving causally without to affect or stop its evolution. For this reason the theory becomes crucial for analyzing the dynamics of the quantum systems, covering the obscure zones where the experiment is irrelevant. The first successful theory was the non- relativistic quantum mechanics which explains how the quantum systems can be measured but taking over the old dynamic of the Newtonian mechanics. The next step was the quantum theory of fields which is a relativistic theory where the interactions are introduced coupling directly the matter fields to the gauge fields according to a given gauge symmetry. Thus one constructed a coherent theory, gifted with appropriate mathematical methods, which is able to explain the quantum phenomenology at the atomic and nuclear scales. Moreover, this theory is indispensable for studying more complicated quantum systems in optics, electronics, solid and plasma physics or even in chemistry and biology. However, despite of the great success of the quantum theory and especially of its Standard Model, this theory is still partially satisfactory in the high energy physics, going to the Planck scale, or at very large scales, in astrophysics and cosmology. This is because in the last few decades the absence of new crucial experimental evidences X Preface forced the quantum theory to evolve independently, following only its internal logic, without to be directed by the experimental reality. In this period one developed many theoretical models in various directions using a large spectrum of new hypotheses and mathematical methods. Many efforts were devoted for building the super-string theory whose principal purpose is to integrate the gravity into the quantum theory. Of a special interest are some particular hypothetic conjectures as, for example, the Higgs mechanism which is the cornerstone of the Standard Model. All these theoretical approaches may be confirmed or invalidated by the new experiments performed using the huge and expensive Large Hadron Collider working today at CERN in Geneva. Even though people waits impatiently for new confirmations and certainties, now it is premature to draw definitive conclusions before finishing to analyze on computer the large amount of data obtained so far. In other words, we do not have yet the experimental criteria we need for selecting definitively the actual theoretical models, obtaining thus a reliable guide in further developments. Under such circumstances, we would like to present here few interesting new directions in which the quantum theory evolves. We start in the first section with some new general ideas in quantum physics and its mathematical methods. The second section is devoted to the modern directions in studying quantum effect in optics and chemistry where the success of the quantum theory is indisputable. We live some specific open problems of the quantum gravity to be presented in the last section. We hope the reader should find useful and attractive information in all of the chapters of this book, written by scientists who obtained recently new remarkable results in their fields of research. Prof. Ion Cotăescu, Head of Department, Director of the Research Center in Theoretical Physics and Gravitation, Department of Theoretical and Computational Physics, Faculty of Physics, West University of Timisoara, Romania . ADVANCES IN QUANTUM THEORY Edited by Ion I. Cotăescu Advances in Quantum Theory Edited by Ion I. Cotăescu Published by InTech Janeza Trdine 9, 51000. directions in studying quantum effect in optics and chemistry where the success of the quantum theory is indisputable. We live some specific open problems of the quantum gravity to be presented in. efforts were devoted for building the super-string theory whose principal purpose is to integrate the gravity into the quantum theory. Of a special interest are some particular hypothetic conjectures