Hamiltonian Mechanics Of Gauge Systems PDF Download
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| Author | : Lev V. Prokhorov |
| Publisher | : Cambridge University Press |
| Total Pages | : 485 |
| Release | : 2011-09-22 |
| Genre | : Science |
| ISBN | : 1139500902 |
Download Hamiltonian Mechanics of Gauge Systems Book in PDF, ePub and Kindle
The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.
| Author | : Marc Henneaux |
| Publisher | : Princeton University Press |
| Total Pages | : 556 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780691037691 |
Download Quantization of Gauge Systems Book in PDF, ePub and Kindle
This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.
| Author | : Heinz J. Rothe |
| Publisher | : World Scientific |
| Total Pages | : 317 |
| Release | : 2010 |
| Genre | : Science |
| ISBN | : 9814299642 |
Download Classical and Quantum Dynamics of Constrained Hamiltonian Systems Book in PDF, ePub and Kindle
This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field?antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. All topics are well illustrated with examples emphasizing points of central interest. The book should enable graduate students to follow the literature on this subject without much problems, and to perform research in this field.
| Author | : Marc Henneaux |
| Publisher | : Princeton University Press |
| Total Pages | : |
| Release | : 2020-06-16 |
| Genre | : Mathematics |
| ISBN | : 0691213860 |
Download Quantization of Gauge Systems Book in PDF, ePub and Kindle
This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.
| Author | : Gaetano Vilasi |
| Publisher | : World Scientific |
| Total Pages | : 457 |
| Release | : 2001 |
| Genre | : Science |
| ISBN | : 9810233086 |
Download Hamiltonian Dynamics Book in PDF, ePub and Kindle
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.
| Author | : L. Mangiarotti |
| Publisher | : World Scientific |
| Total Pages | : 376 |
| Release | : 1998 |
| Genre | : Science |
| ISBN | : 9789810236038 |
Download Gauge Mechanics Book in PDF, ePub and Kindle
This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Non-inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads us to observable physics. The gauge formulation of classical mechanics is extended to quantum mechanics under different reference frames. Special topics on geometric BRST mechanics, relativistic mechanics and others, together with many examples, are also dealt with.
| Author | : Heinz J. Rothe |
| Publisher | : World Scientific |
| Total Pages | : 317 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9814299650 |
Download Classical and Quantum Dynamics of Constrained Hamiltonian Systems Book in PDF, ePub and Kindle
This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.
| Author | : Gaetano Vilasi |
| Publisher | : World Scientific |
| Total Pages | : 460 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9789812386311 |
Download Hamiltonian Dynamics Book in PDF, ePub and Kindle
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations. Contents: Analytical Mechanics: The Lagrangian Coordinates; Hamiltonian Systems; Transformation Theory; The Integration Methods; Basic Ideas of Differential Geometry: Manifolds and Tangent Spaces; Differential Forms; Integration Theory; Lie Groups and Lie Algebras; Geometry and Physics: Symplectic Manifolds and Hamiltonian Systems; The Orbits Method; Classical Electrodynamics; Integrable Field Theories: KdV Equation; General Structures; Meaning and Existence of Recursion Operators; Miscellanea; Integrability of Fermionic Dynamics. Readership: Physicists and mathematicians.
| Author | : G. Sardanashvily |
| Publisher | : World Scientific |
| Total Pages | : 168 |
| Release | : 1995 |
| Genre | : Science |
| ISBN | : 9789810220457 |
Download Generalized Hamiltonian Formalism for Field Theory Book in PDF, ePub and Kindle
In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms. The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical momenta correspond to derivatives of fields with respect to all world coordinates, not only to time. This book is devoted to the application of this formalism to fundamental field models including gauge theory, gravitation theory, and spontaneous symmetry breaking. All these models are constraint ones. Their Euler-Lagrange equations are underdetermined and need additional conditions. In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density. The general procedure for describing constraint systems with quadratic and affine Lagrangian densities is presented.
| Author | : Peter Mann |
| Publisher | : Oxford University Press |
| Total Pages | : 553 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 0198822375 |
Download Lagrangian and Hamiltonian Dynamics Book in PDF, ePub and Kindle
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.
