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Author: Robert Hermann
Publisher: Math-Sci Press
Published: 1973
Total Pages: 132
ISBN-13: 9780915692033
DOWNLOAD EBOOKDownload or read book Energy Momentum Tensors written by Robert Hermann and published by Math-Sci Press. This book was released on 1973 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Somnath Datta
Publisher: World Scientific
Published: 2021-03-02
Total Pages: 384
ISBN-13: 9811228132
DOWNLOAD EBOOKThis book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).The first part explains the main concepts in a layman's language, including STR, the Lorentz transformation, relativistic mechanics. Thereafter the concept of tensors is built up in detail, especially Maxwell's stress tensor with illustrative examples, culminating in the energy-momentum conservation in electromagnetic fields. Mathematical structure of Minkowski's space-time is constructed and explained graphically. The equation of motion is formulated and then illustrated by the example of relativistic rocket. The principle of covariance is explained with the covariant equations of classical electrodynamics. Finally, the book constructs the energy tensor which constitutes the source term in Einstein's field equation, which clears the passage to the GTR.In the book, the concepts of tensors are developed carefully and a large number of numerical examples taken from atomic and nuclear physics. The graphs of important equations are included. This is suitable for studies in classical electrodynamics, modern physics, and relativity.
Download or read book Special Relativity, Tensors, And Energy Tensor: With Worked Problems written by Somnath Datta and published by World Scientific. This book was released on 2021-03-02 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).The first part explains the main concepts in a layman's language, including STR, the Lorentz transformation, relativistic mechanics. Thereafter the concept of tensors is built up in detail, especially Maxwell's stress tensor with illustrative examples, culminating in the energy-momentum conservation in electromagnetic fields. Mathematical structure of Minkowski's space-time is constructed and explained graphically. The equation of motion is formulated and then illustrated by the example of relativistic rocket. The principle of covariance is explained with the covariant equations of classical electrodynamics. Finally, the book constructs the energy tensor which constitutes the source term in Einstein's field equation, which clears the passage to the GTR.In the book, the concepts of tensors are developed carefully and a large number of numerical examples taken from atomic and nuclear physics. The graphs of important equations are included. This is suitable for studies in classical electrodynamics, modern physics, and relativity.
Download or read book Energy Momentum Tensors written by Robert Hermann and published by . This book was released on 1973 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: A. Peres
Publisher:
Published: 1964
Total Pages: 6
ISBN-13:
DOWNLOAD EBOOKIt is shown that the canonical energy-momentum quasitensor differs from the metric energy-momentum tensor density by a complete divergence. Therefore both expressions give the same value for the total energy and momentum of a closed physical system. (Author).
Download or read book ENERGY-MOMENTUM TENSORS. written by A. Peres and published by . This book was released on 1964 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that the canonical energy-momentum quasitensor differs from the metric energy-momentum tensor density by a complete divergence. Therefore both expressions give the same value for the total energy and momentum of a closed physical system. (Author).
Author: John M. Ball
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 477
ISBN-13: 3642599389
DOWNLOAD EBOOKA traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 •••••••••••••••••••••••••••••••••••••••••••••••• 0 ••••• 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 ••••••••••• 0 ••••••••••••••••••• 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.
Download or read book Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids written by John M. Ball and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 •••••••••••••••••••••••••••••••••••••••••••••••• 0 ••••• 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 ••••••••••• 0 ••••••••••••••••••• 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.
Author: Ge Mo-lin
Publisher: World Scientific
Published: 2018-01-05
Total Pages: 384
ISBN-13: 9813237287
DOWNLOAD EBOOKYi-Shi Duan (1927–2016) was one of the world-renowned pioneers in the study of gauge field theory and general relativity. Trained in the former Soviet Union, Prof. Duan returned to China in 1957 to work in Lanzhou University for 60 years. In 1963, he came up with a general co-variant form of the conservation law of the energy-momentum tensor in general relativity. In 1979, he suggested that the gauge potential could be decomposed, which has important implications to gauge field theory. He trained in China a big team of talents in theoretical physics. His contributions to theoretical physics in China have earned him praise from both Professor Shiing-Shen Chern and Professor Chen-Ning Yang. Contents: SU(2) Gauge Theory and Electrodynamics with N Magnetic Monopoles (Yi-Shi Duan and Mo-Lin Ge)Abelian Decomposition of QCD (Y M Cho)How Can We Understand Quark Confinement in Quantum Yang–Mills Theory? (Kei-Ichi Kondo)Asymmetrical Input-output Control in Cavity Quantum Electrodynamics (Yifu Zhu)Energy and Angular Momentum in Gravity Theories (Rong-Gen Cai and Li-Ming Cao)Gravitational Energy and the Gauge Theory Perspective (Chiang-Mei Chen and James M Nester)Energy-Momentum in General Relativity (Xiaoning Wu and Xiao Zhang)Introduction to Extra Dimensions and Thick Braneworlds (Yu-Xiao Liu)Appendices: Chronicle of Prof. Yi-Shi Duan's LifeChronicle of Prof. Yi-Shi Duan's Life (Chinese Version)List of Prof. Yi-Shi Duan's Publications Readership: Graduate students; researchers. Keywords: Yi-Shi Duan;Yang-Mills Theory;General Relativity;Modified Gravity;Gauge Potential Decomposition;Monopole;Energy-Momentum Tenor;Brane World Scenario;Conserved Charge;Cavity Quantum ElectrodynamicsReview: Key Features: Yi-Shi Duan was one of the world-renowned pioneers in the study of gauge field theory and general relativity in ChinaHe trained a big team of talents in theoretical physics in China, such as Mo-Lin Ge, Rong-Gen Cai, etc.His contributions to theoretical physics in China have earned him praise from both Professor S S Chern and Professor C N Yang
Download or read book Memorial Volume For Yi-shi Duan written by Ge Mo-lin and published by World Scientific. This book was released on 2018-01-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Yi-Shi Duan (1927–2016) was one of the world-renowned pioneers in the study of gauge field theory and general relativity. Trained in the former Soviet Union, Prof. Duan returned to China in 1957 to work in Lanzhou University for 60 years. In 1963, he came up with a general co-variant form of the conservation law of the energy-momentum tensor in general relativity. In 1979, he suggested that the gauge potential could be decomposed, which has important implications to gauge field theory. He trained in China a big team of talents in theoretical physics. His contributions to theoretical physics in China have earned him praise from both Professor Shiing-Shen Chern and Professor Chen-Ning Yang. Contents: SU(2) Gauge Theory and Electrodynamics with N Magnetic Monopoles (Yi-Shi Duan and Mo-Lin Ge)Abelian Decomposition of QCD (Y M Cho)How Can We Understand Quark Confinement in Quantum Yang–Mills Theory? (Kei-Ichi Kondo)Asymmetrical Input-output Control in Cavity Quantum Electrodynamics (Yifu Zhu)Energy and Angular Momentum in Gravity Theories (Rong-Gen Cai and Li-Ming Cao)Gravitational Energy and the Gauge Theory Perspective (Chiang-Mei Chen and James M Nester)Energy-Momentum in General Relativity (Xiaoning Wu and Xiao Zhang)Introduction to Extra Dimensions and Thick Braneworlds (Yu-Xiao Liu)Appendices: Chronicle of Prof. Yi-Shi Duan's LifeChronicle of Prof. Yi-Shi Duan's Life (Chinese Version)List of Prof. Yi-Shi Duan's Publications Readership: Graduate students; researchers. Keywords: Yi-Shi Duan;Yang-Mills Theory;General Relativity;Modified Gravity;Gauge Potential Decomposition;Monopole;Energy-Momentum Tenor;Brane World Scenario;Conserved Charge;Cavity Quantum ElectrodynamicsReview: Key Features: Yi-Shi Duan was one of the world-renowned pioneers in the study of gauge field theory and general relativity in ChinaHe trained a big team of talents in theoretical physics in China, such as Mo-Lin Ge, Rong-Gen Cai, etc.His contributions to theoretical physics in China have earned him praise from both Professor S S Chern and Professor C N Yang
Author: Mirjana Dalarsson
Publisher: Academic Press
Published: 2015-07-08
Total Pages: 276
ISBN-13: 0128034017
DOWNLOAD EBOOKTensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. Clearly combines relativity, astrophysics, and cosmology in a single volume Extensive introductions to each section are followed by relevant examples and numerous exercises Presents topics of interest to those researching and studying tensor calculus, the theory of relativity, gravitation, cosmology, quantum cosmology, Robertson-Walker Metrics, curvature tensors, kinematics, black holes, and more Fully revised and updated with 80 pages of new material on relativistic effects, such as relativity of simultaneity and relativity of the concept of distance, amongst other topics Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results
Download or read book Tensors, Relativity, and Cosmology written by Mirjana Dalarsson and published by Academic Press. This book was released on 2015-07-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. Clearly combines relativity, astrophysics, and cosmology in a single volume Extensive introductions to each section are followed by relevant examples and numerous exercises Presents topics of interest to those researching and studying tensor calculus, the theory of relativity, gravitation, cosmology, quantum cosmology, Robertson-Walker Metrics, curvature tensors, kinematics, black holes, and more Fully revised and updated with 80 pages of new material on relativistic effects, such as relativity of simultaneity and relativity of the concept of distance, amongst other topics Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results
Author: Daniel A. Fleisch
Publisher: Cambridge University Press
Published: 2011-09-22
Total Pages: 206
ISBN-13: 9780521171908
DOWNLOAD EBOOKVectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.
Download or read book A Student's Guide to Vectors and Tensors written by Daniel A. Fleisch and published by Cambridge University Press. This book was released on 2011-09-22 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.
Author: Ryosuke Yanagihara
Publisher: Springer Nature
Published: 2021-10-22
Total Pages: 170
ISBN-13: 9811662347
DOWNLOAD EBOOKThe energy momentum tensor (EMT) is one of the most fundamental observables in physics. Recently, a novel method to define EMT on the basis of the gradient-flow formalism has been proposed. It turned out that the EMT operator can be constructed even on the lattice with the method, which enables non-perturbative computations. This approach has been successfully applied to the analyses on thermodynamic quantities. This book presents the study on spatial EMT distributions around static charges via the gradient flow in lattice simulations based on SU(3) Yang-Mills theory. Static charges are employed as probes to explore complex quantum systems, and EMT then characterizes the response of vacuum as well as hot medium under the existence of the charges, which significantly provides profound and novel insights into the non-perturbative phenomena, such as the confinement of quarks. In addition, the book treats the study on the EMT distribution around a magnetic vortex in the Abelian-Higgs model, which is compared with the lattice result. These achievements open up various future studies for revealing non-trivial aspects of the strong interaction. The book also includes well-organized reviews on general properties of EMT, lattice gauge theory and the gradient-flow formalism with its application to the definition of EMT. They are useful for students and young researchers as a brief introduction to this field.
Download or read book Distribution of Energy Momentum Tensor around Static Charges in Lattice Simulations and an Effective Model written by Ryosuke Yanagihara and published by Springer Nature. This book was released on 2021-10-22 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The energy momentum tensor (EMT) is one of the most fundamental observables in physics. Recently, a novel method to define EMT on the basis of the gradient-flow formalism has been proposed. It turned out that the EMT operator can be constructed even on the lattice with the method, which enables non-perturbative computations. This approach has been successfully applied to the analyses on thermodynamic quantities. This book presents the study on spatial EMT distributions around static charges via the gradient flow in lattice simulations based on SU(3) Yang-Mills theory. Static charges are employed as probes to explore complex quantum systems, and EMT then characterizes the response of vacuum as well as hot medium under the existence of the charges, which significantly provides profound and novel insights into the non-perturbative phenomena, such as the confinement of quarks. In addition, the book treats the study on the EMT distribution around a magnetic vortex in the Abelian-Higgs model, which is compared with the lattice result. These achievements open up various future studies for revealing non-trivial aspects of the strong interaction. The book also includes well-organized reviews on general properties of EMT, lattice gauge theory and the gradient-flow formalism with its application to the definition of EMT. They are useful for students and young researchers as a brief introduction to this field.
Download or read book Energy-momentum Tensor, Stability and the D-term in Soliton Models written by Manuel Mai and published by . This book was released on 2009 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
