Dual-Spin Dirac Equation and Maxwell's Equations PDF Download
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Author: Xiafu Zhang
Publisher: Dorrance Publishing
ISBN:
Category : Science
Languages : en
Pages : 367
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Book Description
When studying the Dirac equation and Maxwell's equations, replacing the current second-order Pauli spin matrices with fourth-order spin matrices reveals that the Dirac equation contains a pair of spins, and the Maxwell’s equations contain spins and Runge-Lenz vector. This book refers to the pair of spins as "dual-spin". The dual-spin matrices are the main components of these equations. Based on the existence of infinite representations of dual-spin matrices, they can be expressed as operators. This book proposes a new representation for Dirac equation and the Maxwell’s equations using these dual-spin operators, and mathematically proves its existence. With the new representation, this book also demonstrates the harmonious unity of the internal structure of the equations and the inherent connection between the two equations, and introduces new symmetries, new solution methods, as well as new approaches to Lorentz transformations by this dual-spin representation. Furthermore, the original Dirac equation only contained one spin, but the author has discovered that there are two spins, which is a breakthrough in cognition.
Author: Xiafu Zhang
Publisher: Dorrance Publishing
ISBN:
Category : Science
Languages : en
Pages : 367
Get Book Here
Book Description
When studying the Dirac equation and Maxwell's equations, replacing the current second-order Pauli spin matrices with fourth-order spin matrices reveals that the Dirac equation contains a pair of spins, and the Maxwell’s equations contain spins and Runge-Lenz vector. This book refers to the pair of spins as "dual-spin". The dual-spin matrices are the main components of these equations. Based on the existence of infinite representations of dual-spin matrices, they can be expressed as operators. This book proposes a new representation for Dirac equation and the Maxwell’s equations using these dual-spin operators, and mathematically proves its existence. With the new representation, this book also demonstrates the harmonious unity of the internal structure of the equations and the inherent connection between the two equations, and introduces new symmetries, new solution methods, as well as new approaches to Lorentz transformations by this dual-spin representation. Furthermore, the original Dirac equation only contained one spin, but the author has discovered that there are two spins, which is a breakthrough in cognition.
Author: Waldyr A. Rodrigues
Publisher: Springer Science & Business Media
ISBN: 3540712925
Category : Mathematics
Languages : en
Pages : 452
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Book Description
This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories. All calculation procedures are illustrated by many exercises that are solved in detail.
Author: Akhlesh Lakhtakia
Publisher: World Scientific
ISBN: 9814504157
Category : Science
Languages : en
Pages : 559
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Book Description
Beltrami fields exist commonly in all areas of wave theory. In particular, Beltrami fields are necessary to analyze electromagnetic wave propagation in isotropic chiral materials, numerous examples of which are found in organic chemistry. Artificial chiral composites are evaluated for electromagnetic engineering purposes as well. In this book a comprehensive analysis of electromagnetic fields in chiral materials has been made.
Author: Waldyr A. Rodrigues, Jr
Publisher: Springer
ISBN: 3319276379
Category : Science
Languages : en
Pages : 592
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Book Description
This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solutions, the comprehensive list of mathematical symbols, and the list of acronyms and abbreviations are provided for self-study for students as well as for classes. From the reviews of the first edition: “The text is written in a very readable manner and is complemented with plenty of worked-out exercises which are in the style of extended examples. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
Author: Richard L Amoroso
Publisher: World Scientific
ISBN: 9814462950
Category : Science
Languages : en
Pages : 412
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Book Description
The Maxwell, Einstein, Schrödinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal their richness and continued importance for advancing fundamental Physics. If M-Theory is to keep its promise of defining the ultimate structure of matter and spacetime, it is only through the topological configurations of additional dimensionality (or degrees of freedom) that this will be possible. Stretching the exploration of complex space through all of the main equations of Physics should help tighten the noose on “the” fundamental theory. This kind of exploration of higher dimensional spacetime has for the most part been neglected by M-theorists and physicists in general and is taken to its penultimate form here.
Author: Michel van Veenendaal
Publisher: John Wiley & Sons
ISBN: 1119913217
Category : Science
Languages : en
Pages : 372
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Book Description
Unique senior undergraduate/graduate level textbook on quantum mechanics that employs an intuitive, geometry-driven approach to the subject Geometric Quantum Mechanics is a textbook for quantum mechanics at the senior undergraduate and graduate level and follows a unique approach to the material. The first chapter starts with the discussion of the properties of space leading to an understanding of operator techniques, Pauli matrices, spinors, quantum angular momentum, etc. Techniques from geometric algebra are frequently employed leading to more intuitive insights into the concepts. The second chapter extends the results to spacetime. The study of the motion in and the production of electromagnetic fields leads to the Lorentz and Maxwell equations, respectively. The nonrelativistic limit leads to the Schrödinger/Heisenberg equations. This provides an overview how different fields are linked to each other. The following chapters discuss applications of quantum mechanics. This covers a very broad area of physics showing how the ideas from quantum mechanics affect different fields. These are subdivided into chapters on single-particle problems, many-particle systems, and collective and emergent phenomena. The coverage includes the fundamental forces, atoms, molecules and solids, nuclear and particle physics, mass generation and the Higgs field, superconductivity, superfluidity, etc. The book restricts itself to the essence of these topics allowing the reader to understand how quantum mechanics impacts modern-day physics and chemistry. It appeals to instructors and students due to its different approach with its extensive use of geometric algebra and the broad range of modern applications.
Author: Herbert Martin Fried
Publisher: World Scientific
ISBN: 9814542733
Category : Science
Languages : en
Pages : 397
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Book Description
Contents: Basic Concepts and Consequences of Stochastic Vacuum Model (H G Dosch)Variational Approximations for Correlation Functions in Quantum Field Theories (C Martin)SU(2) Gauge Theory in Covariant (Maximal) Abelian Gauges (M Schaden)The Vacuum Wave Function in Supersymmetric Matrix Theory (C M Sommerfield)HERA Results on Elastic Hadronic and Sub-Hadronic Diffraction (G Knies)Deriving Effective Transport Equations for Non-Abelian Plasmas (D F Litim)Aspects of Non-Commutativity in ADS/CFT (A Jevicki)Thermal Field Theory in Equilibrium (J O Andersen)Puzzling Aspects of Hot Quantum Fields (T Grandou)DIS Results from HERA (C M Ginsburg)Electroproduction of Vector Mesons (T Teubner)New Developments in Cosmology (J W Moffat)Heavy-Light Physics from Lattice NRQCD (T Onogi)Non-Relativistic Effective Theory for Perturbative Heavy Quark-Antiquark Systems (A H Hoang)The Spin Dependence of Swift Proton Collisions (N H Buttimore)Numerical Investigation of Domain-Wall QCD on CP-PACS (S Aoki)When is It Possible to Use Perturbation Technique in Field Theory? (T N Truong)and other papers Readership: Researchers in high energy physics. Keywords:
Author:
Publisher:
ISBN:
Category : Nuclear energy
Languages : en
Pages : 722
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Book Description
Author: Michael Atiyah
Publisher: Oxford University Press
ISBN: 9780198532798
Category : Biography & Autobiography
Languages : en
Pages : 728
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Book Description
This is a collection of the works of Michael Atiyah, a well-established mathematician and winner of the Fields Medal. It is thematically divided into volumes; this one discusses gauge theory, a current topic of research.
Author: Robert J. Gould
Publisher: Princeton University Press
ISBN: 0691215847
Category : Science
Languages : en
Pages : 312
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Book Description
This book provides an understanding of the theoretical foundations for the calculation of electromagnetic processes. Photon production processes are particularly important in astrophysics, since almost all of our knowledge of distant astronomical objects comes from the detection of radiation from these sources. Further, the conditions therein are extremely varied and a wide variety of naturally occurring electromagnetic phenomena can be described by limiting forms of the basic theory. The first chapter reviews some basic principles that are the underpinnings for a general description of electromagnetic phenomena, such as special relativity and, especially, relativistic covariance. Classical and quantum electrodynamics (QED) are then formulated in the next two chapters, followed by applications to three basic processes (Coulomb scattering, Compton scattering, and bremsstrahlung). These processes are related to other phenomena, such as pair production, and the comparisons are discussed. A unique feature of the book is its thorough discussion of the nonrelativistic limit of QED, which is simpler than the relativistic theory in its formulation and applications. The methods of the relativistic theory are introduced and applied through the use of notions of covariance, to provide a shorter path to the more general theory. The book will be useful for graduate students working in astrophysics and in certain areas of particle physics.
