Advances in Quantum Theory

260 Pages·2012·3.905 MB·English

by  I. Cotaescu

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
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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 [email protected]

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