Geometry of the Fundamental Interactions

Geometry of the Fundamental Interactions
Author: M. D. Maia
Publisher: Springer Science & Business Media
Total Pages: 182
Release: 2011-06-14
Genre: Science
ISBN: 1441982736

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The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles. Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field. This book presents an account of the geometrical properties of gauge field theory, while trying to keep the equilibrium between mathematics and physics. At the end we will introduce a similar approach to the gravitational field.

Infinite Dimensional Geometry, Noncommutative Geometry, Operator Algebras And Fundamental Interactions - Proceedings Of The First Caribbean Spring School Of Mathematics And Theoretical Physics

Infinite Dimensional Geometry, Noncommutative Geometry, Operator Algebras And Fundamental Interactions - Proceedings Of The First Caribbean Spring School Of Mathematics And Theoretical Physics
Author: Robert Coquereaux
Publisher: World Scientific
Total Pages: 414
Release: 1995-06-28
Genre:
ISBN: 9814549320

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Geometry and Theoretical Physics

Geometry and Theoretical Physics
Author: Joachim Debrus
Publisher: Springer Science & Business Media
Total Pages: 333
Release: 2012-12-06
Genre: Science
ISBN: 3642763537

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The interaction between geometry and theoretical physics has often been very fruitful. A highlight in this century was Einstein's creation of the theory of general relativity. Equally impressive was the recognition, starting from the work of Yang and Mills and culminating in the Weinberg-Salam theory of the electroweak interaction and quantum chromodynamics, that the fundamental interactions of elementary particles are governed by gauge fields, which in ma thematical terms are connections in principal fibre bundles. Theoretical physi cists became increasingly aware of the fact that the use of modern mathematical methods may be necessary in the treatment of problems of physical interest. Since some of these topics are covered at most summarily in the usual curricu lum, there is a need for extra-curricular efforts to provide an opportunity for learning these techniques and their physical applications. In this context we arranged a meeting at the Physikzentrum Bad Ronnef 12-16 February 1990 on the subject "Geometry and Theoretical Physics", in the series of physics schools organized by the German Physical Society. The participants were graduate students from German universities and research institutes. Since the meeting occurred only a short time after freedom of travel between East and West Germany became a reality, this was for many from the East the first opportunity to attend a scientific meeting in the West, and for many from the West the first chance to become personally acquainted with colleagues from the East.

An Introduction to Geometrical Physics

An Introduction to Geometrical Physics
Author: Aldrovandi Ruben
Publisher: World Scientific
Total Pages: 844
Release: 2016-10-07
Genre: Science
ISBN: 9813146834

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This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear. The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students. In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.

Geometry at the Quantum Scale

Geometry at the Quantum Scale
Author: Marcos D. Maia
Publisher: Springer
Total Pages: 0
Release: 2024-10-20
Genre: Science
ISBN: 9783031611964

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This book presents a geometric perspective on the ever-expanding landscape of (often unfalsifiable) theories of fundamental physics that have emerged from the beginning of the twentieth century until the present day. The authors present a summary of the landmark results, and the assumptions needed to obtain them, viewed with the common philosophy that many difficulties in fundamental physics could be elucidated by an understanding of the geometrical language of quantum physics, motivated initially by the geometric implications of the ‘t Hooft—Veltman renormalization of gauge fields. The geometrical language underpinning this worldview is affine geometry, a common feature of the four known fundamental interactions, where affinity between observables is mediated by a fundamental interaction, as in the example of local gauge fields in quantum field theory. The same can be said of Einstein’s gravitational field based on the (pseudo-)Riemannian geometry where the affinity comes from the metric. Such notions allow one to interpret affinity at the quantum scale of observations, and consider questions such as: What is the meaning of the Planck regime? What is the meaning of the cosmological principle? What is quantum gravity? Is the Newtonian gravitational constant really universal? Is information lost in quantum gravity? The book reviews fundamental background material, presents manifold insights into the geometrical nature of quantum physics and cosmology, suggests promising avenues for future research, and in places even proposes experimental tests. It will be of interest to high energy physicists, cosmologists, mathematicians, and philosophers of science.

The Fundamental Interaction

The Fundamental Interaction
Author: J. Debrus
Publisher: Springer Science & Business Media
Total Pages: 246
Release: 2012-12-06
Genre: Science
ISBN: 1461595223

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A meeting was held at the Physics Centre in Bad Honnef from Feb. 16-20, 1987 on the subject "The Fundamental Interaction: Geometrical Trends". This meeting was in the series of Physics Schools organized by the German Physical Society. The participants were mainly younger scientists and graduate students: physicists, mathematicians and astronomers from the Federal Republic of Germany; there were also participants from Austria, the Netherlands and Switzerland. The purpose of the meeting was to introduce the participants to modern methods of mathematics and field theory which are increasingly being used in current elementary particle research. An outstanding feature of the school was the fact that each lecturer really made an effort to present his material at an introductory level, which could be followed by people with the usual degree level qualifications and which, nevertheless, then led up to the level of contemporary specialized literature. We hope that the published volume will make these lectures, which taken together give a unified overview of the recent developments leading up to the current world-view in modern theoretical physics, available to a wider audience. We wish to thank the lecturers, who besides the formal lectures devoted their time to discussions with the participants throughout the duration of the School. We are also grateful to the staff of the Physics Centre for their organizational assistance, and to the participants, whose active interest made the meeting a success. The entire manuscript was efficiently typed by Manfred Krafczyk at the University of Dortmund.

Energy and Geometry

Energy and Geometry
Author: Fabio Cardone
Publisher: World Scientific
Total Pages: 161
Release: 2004
Genre: Science
ISBN: 9812387285

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Special Relativity (SR) is essentially grounded on the properties of space-time, i.e. isotropy of space and homogeneity of space and time (as a consequence of the equivalence of inertial frames) and on the Galilei principle of relativity.

Duality of Time

Duality of Time
Author: Mohamed Haj Yousef
Publisher: Mohamed Haj Yousef
Total Pages: 411
Release: 2018-01-01
Genre: Science
ISBN: 1539579204

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The Duality of Time Theory is the result of more than two decades of ceaseless investigation and searching through ancient manuscripts of concealed philosophies and mystical traditions, comparing all that with the fundamental results of modern physics and cosmology, until all the contradicting jigsaw pieces were put together into this brilliant portrait. Without the overwhelming proofs and strong confirmations that accumulated over time, it would have been impossible to pursue this long research path, as it was extremely challenging to appreciate the unfathomable secret of time and the consequences of the ongoing perpetual creation of space, that result from the Single Monad Model of the Cosmos. The complex-time geometry of the Duality of Time Theory explains how the physical dimensions of space are sequentially being re-created in the inner levels of time, which makes the outward time genuinely imaginary with respect to the inner real levels. This is easily expressed in terms of the hyperbolic split-complex numbers, that characterize the Relativistic Lorentzian Symmetry. This will have deep implications because space-time has become naturally quantized in a way that explains and unites all the three principles of Relativity, leading to full Quantum Field Theory of Gravity, as well as explaining all the other fundamental interactions in terms of the new granular space-time geometry. This ultimate unification will solve many persisting problems in physics and cosmology. The homogeneity problem, for example, will instantly cease, since the Universe, no matter how large it could be, is re-created sequentially in the inner time, so all the states are updated and synchronized before they appear in the outer level that we encounter. Furthermore, the Duality of Time does not only unify all the fundamental interactions in terms of its genuinely-complex time-time geometry, but it unifies this whole physical world with the two other even more fundamental domains of the psychical and spiritual worlds. All these three conclusive and complementary realms are constructed on the same concept of space-time geometry that together form one single absolute and perfectly symmetrical space. This particular subject is treated at length in the Third Volume of this book series - the Ultimate Symmetry, which explores how the apparent physical and metaphysical multiplicity is emerging from the absolute Oneness of Divine Presence, descending through four fundamental levels of symmetry: ultimate, hyper, super and normal. Among many other astonishing consequences, this astounding conclusion means that the psychical world is composed of atoms and molecules that are identical with the physical world except that they are evolving in orthogonal time direction. It may appear initially impossible to believe how the incorporeal worlds may have the same atomic structure as the physical world, but it is more appropriate to say that physical structures are eventually incorporeal, because they become various wave phenomena and energy interactions as soon as we dive into their microscopic level, as it is now confirmed by Quantum Field Theories. In the Duality of Time Theory, since rigid space is created sequentially in the inner time, energy may become negative, imaginary and even multidimensional, which simply means that all things in creation are various kinds of energy moments that are spreading on different intersecting dimensions of time; so not only mass and energy are equivalent, but also charge and all other physical and metaphysical entities are interconvertible types of energy, including consciousness and information.

Geometry and Theoretical Physics

Geometry and Theoretical Physics
Author: Joachim Debrus
Publisher: Springer
Total Pages: 323
Release: 1991-09-10
Genre: Science
ISBN: 9783540535706

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The interaction between geometry and theoretical physics has often been very fruitful. A highlight in this century was Einstein's creation of the theory of general relativity. Equally impressive was the recognition, starting from the work of Yang and Mills and culminating in the Weinberg-Salam theory of the electroweak interaction and quantum chromodynamics, that the fundamental interactions of elementary particles are governed by gauge fields, which in ma thematical terms are connections in principal fibre bundles. Theoretical physi cists became increasingly aware of the fact that the use of modern mathematical methods may be necessary in the treatment of problems of physical interest. Since some of these topics are covered at most summarily in the usual curricu lum, there is a need for extra-curricular efforts to provide an opportunity for learning these techniques and their physical applications. In this context we arranged a meeting at the Physikzentrum Bad Ronnef 12-16 February 1990 on the subject "Geometry and Theoretical Physics", in the series of physics schools organized by the German Physical Society. The participants were graduate students from German universities and research institutes. Since the meeting occurred only a short time after freedom of travel between East and West Germany became a reality, this was for many from the East the first opportunity to attend a scientific meeting in the West, and for many from the West the first chance to become personally acquainted with colleagues from the East.