Download or read book Quaternionic Quantum Mechanics and Quantum Fields written by Stephen L. Adler and published by Oxford University Press. This book was released on 1995-04-27 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been known since the 1930s that quantum mechanics can be formulated in quaternionic as well as complex Hilbert space. But systematic work on the quaternionic extension of standard quantum mechanics has scarcely begun. Authored by a world-renowned theoretical physicist, this book signals a major conceptual advance and gives a detailed development and exposition of quaternionic quantum mechanics for the purpose of determining whether quaternionic Hilbert space is the appropriate arena for the long sought-after unification of the standard model forces with gravitation. Significant results from earlier literature, together with many new results obtained by the author, are integrated to give a coherent picture of the subject. The book also provides an introduction to the problem of formulating quantum field theories in quaternionic Hilbert space. The book concludes with a chapter devoted to discussions on where quaternionic quantum mechanics may fit into the physics of unification, experimental and measurement theory issues, and the many open questions that still challenge the field. This well-written treatise is a very significant contribution to theoretical physics. It will be eagerly read by a wide range of physicists.
Download or read book Quaternionic Quantum Mechanics and Quantum Fields written by Stephen L. Adler and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a conceptualization of quantum mechanics, using quaternions instead of complex numbers, the author gives a systematic treatment of quaternionic quantum mechanics paralleling the standard textbook treatment of complex quantum mechanics.
Download or read book Quantum Mechanics and Gravity written by Mendel Sachs and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a paradigm change in modern physics from the philosophy and mathematical expression of the quantum theory to those of general relativity. The approach applies to all domains - from elementary particles to cosmology. The change is from the positivistic views in which atomism, nondeterminism and measurement are fundamental, to a holistic view in realism, wherein matter - electrons, galaxies, - are correlated modes of a single continuum, the universe. A field that unifies electromagnetism, gravity and inertia is demonstrated explicitly, with new predictions, in terms of quaternion and spinor field equations in a curved spacetime. Quantum mechanics emerges as a linear, flatspace approximation for the equations of inertia in general relativity.
Download or read book Noncommutative Geometry Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Download or read book Theory and Phenomenology of Quaternionic and Locally Complex Quantum Field Theory written by Steven P. Brumby and published by . This book was released on 1997 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies in Quaternionic Quantum Mechanics written by Chaddesley Gerard Nash and published by . This book was released on 1987 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics of the Universe written by Mendel Sachs and published by World Scientific. This book was released on 2010 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new approach to the subject of cosmology. It fully exploits Einstein?s theory of general relativity. It is found that the most general formal expression of the theory replaces the (10-component) tensor formalism with a (16-component) quaternion formalism. This leads to a unified field theory, where one field incorporates gravitation and electromagnetism. The theory predicts an oscillating universe cosmology with a spiral configuration. Dark matter is explained in terms of a sea of particle?antiparticle pairs, each in a particular (derived) ground state. This leads to an explanation for the separation between matter and antimatter in the universe. There is a brief discussion of black holes and pulsars. The final chapter delves into philosophical considerations such as the different types of ?truth?, positivism versus realism and a discussion of the role of the Mach principle in physics and cosmology.
Download or read book Quantum Mechanics of Fundamental Systems 1 written by Claudio Teitelboim and published by Springer Science & Business Media. This book was released on 1988-07-31 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adventures in Theoretical Physics written by Stephen L. Adler and published by World Scientific. This book was released on 2006 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the period 1964-1972, Stephen L. Adler wrote seminal papers on high energy neutrino processes, current algebras, soft pion theorems, sum rules, and perturbation theory anomalies that helped lay the foundations for our current standard model of elementary particle physics. These papers are reprinted here together with detailed historical commentaries describing how they evolved, their relation to other work in the field, and their connection to recent literature. Later important work by Dr. Adler on a wide range of topics in fundamental theory, phenomenology, and numerical methods, and their related historical background, is also covered in the commentaries and reprints. This book will be a valuable resource for graduate students and researchers in the fields in which Dr. Adler has worked, and for historians of science studying physics in the final third of the twentieth century, a period in which an enduring synthesis was achieved.
Download or read book Second International A D Sakharov Conference On Physics written by Igor Michailovich Dremin and published by World Scientific. This book was released on 1997-04-15 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the Second International A D Sakharov Conference on Physics, more than 200 physicists from many countries gathered together to celebrate what would have been the 75th birthday of the distinguished physicist and world figure Andrei Sakharov. This tradition had begun five years earlier, soon after his death.The conference was unique: it brought together leading scientists working in seemingly different fields, which were nevertheless among Sakharov's interests. Participants discussed the status and perspectives of research in high-energy physics, cosmology, astrophysics, classical and quantum gravity, plasma physics, nuclear physics, and extreme states of matter. The conference provided a unique opportunity for the participants to find and discuss common points of interest. The proceedings are evidence of the great variety of topics.Talks were given by distinguished physicists such as S Drell, L Okun, R Wilson, A D Linde, C W Misner, N A Popov, S L Adler, B DeWitt, M Kaku, J H Schwarz, A Zamolodchikov and E S Fradkin.
Download or read book Proceedings of the Second International A D Sakharov Conference on Physics written by Igor Michailovich Dremin and published by World Scientific. This book was released on 1997 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Field Theory A Tourist Guide for Mathematicians written by Gerald B. Folland and published by American Mathematical Soc.. This book was released on 2021-02-03 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam–Weinberg model of electromagnetic and weak interactions.
Download or read book Selected Topics In Quantum Field Theory And Mathematical Physics written by J Fischer and published by World Scientific. This book was released on 1990-05-01 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Towards Realism Interpretation ofWave Mechanics based on Maxwell Equations in Quaternion Space and some implications including Smarandache s Hypothesis written by Victor Christianto and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: From time to time, some eminent physicists commenced to ask: What is the reality behind quantum mechanical predictions? Is there a realism interpretation of Quantum Physics? This paper is intended to explore such a possibility of a realism interpretation of QM, based on a derivation of Maxwell equations in Quaternion Space. In this regards, we begin with Quaternion space and its respective Quaternion Relativity (it also may be called as Rotational Relativity) as it has been discussed in several papers including [1]. The purpose of the present paper is to review our previous derivation of Maxwell equations in Q-space [17], with discussion on some implications. First, we will review our previous results in deriving Maxwell equations using Dirac decomposition, introduced by Gersten (1999). Then we will shortly make a few remark on helical solutions of Maxwell equations, Smarandache’s Hypothesis and possible cosmological entanglement. Further observations are of course recommended to refute or verify some implications of this proposition.
Download or read book Unified Field Mechanics Natural Science Beyond The Veil Of Spacetime Proceedings Of The Ix Symposium Honoring Noted French Mathematical Physicist Jean pierre Vigier written by Richard L Amoroso and published by World Scientific. This book was released on 2015-09-08 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unified Field Mechanics, the topic of the 9th international symposium honoring noted French mathematical physicist Jean-Pierre Vigier cannot be considered highly speculative as a myopic critic might surmise. The 8th Vigier Symposium proceedings 'The Physics of Reality' should in fact be touted as a companion volume because of its dramatic theoretical Field Mechanics in additional dimensionality. Many still consider the Planck-scale zero-point field stochastic quantum foam as the 'basement of reality'. This could only be considered true under the limitations of the Copenhagen interpretation of quantum theory. As we enter the next regime of Unified Field Mechanics we now know that the energy-dependent Einstein-Minkowski manifold called spacetime has a finite radius beyond which a large-scale multiverse beckons. So far a battery of 14 experiments has been designed to falsify the model. When the 1st is successfully performed, a revolution in Natural Science will occur! This volume strengthens and expands the theoretical and experimental basis for that immanent new age.
Download or read book Rotations Quaternions and Double Groups written by Simon L. Altmann and published by Courier Corporation. This book was released on 2013-04-09 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems. Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.
Download or read book On The Role Of Division Jordan And Related Algebras In Particle Physics written by Feza Gursey and published by World Scientific. This book was released on 1996-11-22 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the role of some associative and non-associative algebras, remarkable by their ubiquitous appearance in contemporary theoretical physics, particularly in particle physics. It concerns the interplay between division algebras, specifically quaternions and octonions, between Jordan and related algebras on the one hand, and unified theories of the basic interactions on the other. Selected applications of these algebraic structures are discussed: quaternion analyticity of Yang-Mills instantons, octonionic aspects of exceptional broken gauge, supergravity theories, division algebras in anyonic phenomena and in theories of extended objects in critical dimensions. The topics presented deal primarily with original contributions by the authors.
