| Description |
1 online resource (xvi, 573 pages) : illustrations |
| Series |
Unitext, 2038-5714 |
|
Unitext.
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| Contents |
Machine generated contents note: 1. Special Relativity -- 1.1. Principle of Relativity -- 1.1.1. Galilean Relativity in Classical Mechanics -- 1.1.2. Invariance of Classical Mechanics Under Galilean Transformations -- 1.2. Speed of Light and Electromagnetism -- 1.3. Lorentz Transformations -- 1.4. Kinematic Consequences of the Lorentz Transformations -- 1.5. Proper Time and Space -- Time Diagrams -- 1.5.1. Space -- Time and Causality -- 1.6. Composition of Velocities -- 1.6.1. Aberration Revisited -- 1.7. Experimental Tests of Special Relativity -- Reference -- 2. Relativistic Dynamics -- 2.1. Relativistic Energy and Momentum -- 2.1.1. Energy and Mass -- 2.1.2. Nuclear Fusion and the Energy of a Star -- 2.2. Space -- Time and Four-Vectors -- 2.2.1. Four-Vectors -- 2.2.2. Relativistic Theories and Poincare Transformations -- Reference -- 3. Equivalence Principle -- 3.1. Inertial and Gravitational Masses -- 3.2. Tidal Forces -- 3.3. Geometric Analogy -- 3.4. Curvature -- 3.4.1. Elementary Approach to the Curvature -- 3.4.2. Parallel Transport -- 3.4.3. Tidal Forces and Space -- Time Curvature -- 3.5. Motion of a Particle in Curved Space -- Time -- 3.5.1. Newtonian Limit -- 3.5.2. Time Intervals in a Gravitational Field -- 3.5.3. Einstein Equation -- Reference -- 4. Poincare Group -- 4.1. Linear Vector Spaces -- 4.1.1. Covariant and Contravariant Components -- 4.2. Tensors -- 4.3. Tensor Algebra -- 4.4. Rotations in Three-Dimensions -- 4.5. Groups of Transformations -- 4.5.1. Lie Algebra of the SO(3) Group -- 4.6. Principle of Relativity and Covariance of Physical Laws -- 4.7. Minkowski Space -- Time and Lorentz Transformations -- 4.7.1. General Form of (Proper) Lorentz Transformations -- 4.7.2. Poincare Group -- Reference -- 5. Maxwell Equations and Special Relativity -- 5.1. Electromagnetism in Tensor Form |
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Note continued: 5.2. Lorentz Force -- 5.3. Behavior of E and B Under Lorentz Transformations -- 5.4. Four-Current and the Conservation of the Electric Charge -- 5.5. Energy-Momentum Tensor -- 5.6. Four-Potential -- 5.6.1. Spin of a Plane Wave -- 5.6.2. Large Volume Limit -- Reference -- 6. Quantization of the Electromagnetic Field -- 6.1. Electromagnetic Field as an Infinite System of Harmonic Oscillators -- 6.2. Quantization of the Electromagnetic Field -- 6.3. Spin of the Photon -- Reference -- 7. Group Representations and Lie Algebras -- 7.1. Lie Groups -- 7.2. Representations -- 7.3. Infinitesimal Transformations and Lie Algebras -- 7.4. Representation of a Group on a Field -- 7.4.1. Invariance of Fields -- 7.4.2. Infinitesimal Transformations on Fields -- 7.4.3. Application to Non-Relativistic Quantum Mechanics -- Reference -- 8. Lagrangian and Hamiltonian Formalism -- 8.1. Dynamical System with a Finite Number of Degrees of Freedom -- 8.1.1. Action Principle -- 8.1.2. Lagrangian of a Relativistic Particle -- 8.2. Conservation Laws -- 8.2.1. Noether Theorem for a System of Particles -- 8.3. Hamiltonian Formalism -- 8.4. Canonical Transformations and Conserved Quantities -- 8.4.1. Conservation Laws in the Hamiltonian Formalism -- 8.5. Lagrangian and Hamiltonian Formalism in Field Theories -- 8.5.1. Functional Derivative -- 8.5.2. Hamilton Principle of Stationary Action -- 8.6. Action of the Electromagnetic Field -- 8.6.1. Hamiltonian for an Interacting Charge -- 8.7. Symmetry and the Noether Theorem -- 8.8. Space -- Time Symmetries -- 8.8.1. Internal Symmetries -- 8.9. Hamiltonian Formalism in Field Theory -- 8.9.1. Symmetry Generators in Field Theories -- Reference -- 9. Quantum Mechanics Formalism -- 9.1. Introduction -- 9.2. Wave Functions, Quantum States and Linear Operators -- 9.3. Unitary Operators |
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Note continued: 11.7.1. Indefinite Metric and Subsidiary Conditions -- 11.7.2. Poincare Transformations and Discrete Symmetries -- 11.8. Quantum Electrodynamics -- Reference -- 12. Fields in Interaction -- 12.1. Interaction Processes -- 12.2. Kinematics of Interaction Processes -- 12.2.1. Decay Processes -- 12.2.2. Scattering Processes -- 12.3. Dynamics of Interaction Processes -- 12.3.1. Interaction Representation -- 12.3.2. Scattering Matrix -- 12.3.3. Two-Particle Phase-Space Element -- 12.3.4. Optical Theorem -- 12.3.5. Natural Units -- 12.3.6. Wick's Theorem -- 12.4. Quantum Electrodynamics and Feynman Rules -- 12.4.1. External Electromagnetic Field -- 12.5. Amplitudes in the Momentum Representation -- 12.5.1. Moller Scattering -- 12.5.2. Comment on the Role of Virtual Photons -- 12.5.3. Bhabha and Electron-Muon Scattering -- 12.5.4. Compton Scattering and Feynman Rules -- 12.5.5. Gauge Invariance of Amplitudes -- 12.5.6. Interaction with an External Field -- 12.6. Cross Sections -- 12.6.1. Bahbha Scattering -- 12.6.2. Compton Scattering -- 12.7. Divergent Diagrams -- 12.8. Pedagogical Introduction to Renormalization -- 12.8.1. Power Counting and Renormalizability -- 12.8.2. Electron Self-Energy Part -- 12.8.3. Photon Self-Energy -- 12.8.4. Vertex Part -- 12.8.5. One-Loop Renormalized Lagrangian -- 12.8.6. Electron Anomalous Magnetic Moment -- Reference |
| Summary |
This books aims at filling a gap between the basics courses of classical and quantum mechanics and advanced courses of (relativistic) quantum mechanics and field theory. Particular emphasis is given to the role of symmetry in modern theoretical physics. For this reason this book is particularly suited to those students who are interested in a deeper knowledge of modern developments in elementary particle physics and relativity, even if they choose not to specialize in this branch of research. This target of readers includes, besides experimental and applied physicists, also those engineers who need advanced notions of theoretical high energy physics, in view of future research activity in the field theory approach to condensed matter, in accelerator physics and in all those modern technology sectors which require a more advanced and sophisticated theoretical physics background. Courses motivated by these objectives are present in several polytechnic institutes around the world. The last chapters of this book, in particular, are of particular importance to those engineers who plan to work in high energy physics research centres, like LHC at CERN, or to collaborate to experiments on the revelation of gravitational waves. As far as engineering is concerned, it is important to stress that elementary Special and General Relativity courses are often absent in their curricula |
| Analysis |
Physics |
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Quantum theory |
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Mathematical physics |
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Quantum Physics |
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Mathematical Methods in Physics |
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Elementary Particles, Quantum Field Theory |
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Classical and Quantum Gravitation, Relativity Theory |
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Cosmology |
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kwantumtheorie |
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deeltjes |
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particles |
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fysica |
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toegepaste wiskunde |
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applied mathematics |
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quantumfysica |
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astronomie |
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astronomy |
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Physics (General) |
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Fysica (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
| Subject |
Physics.
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Quantum theory.
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Mathematical physics.
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Physics
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Quantum Theory
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physics.
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Physique.
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Astronomie.
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Mathematical physics
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Physics
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Quantum theory
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| Form |
Electronic book
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| Author |
Trigiante, Mario.
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| ISBN |
9788847015043 |
|
8847015049 |
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