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This book presents a review of various issues related to Lorentz symmetry breaking. Explicitly, we consider (i) motivations for introducing Lorentz symmetry breaking, (ii) classical aspects of Lorentz-breaking field theory models including typical forms of Lorentz-breaking additive terms, wave propagation in Lorentz-breaking theories, and mechanisms for breaking the Lorentz symmetry; (iii) quantum corrections in Lorentz-breaking theories, especially the possibilities for perturbation generating the most interesting Lorentz-breaking terms; (iv) correspondence between non-commutative field theories and Lorentz symmetry breaking; (v) supersymmetric Lorentz-breaking theories; and (vi) Lorentz symmetry breaking in a curved space-time. We close the book with the review of experimental studies of Lorentz symmetry breaking. The importance and relevance of these topics are explained, first, by studies of limits of applicability of the Lorentz symmetry, second, by searches of the possible extensions of the standard model, including the Lorentz-breaking ones, and need to study their properties, third, by the relation between Lorentz symmetry breaking with string theory, fourth, by the problem of formulating a consistent quantum gravity theory, so that various modified gravity models are to be examined.

Lorentz transformations. --- Special relativity (Physics) --- Transformations (Mathematics)

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Nuclear spin. --- Quantum field theory. --- Champs, Th eorie quantique des. --- Lorentz, Groupes de. --- Lorentz, Transformations de. --- Ondes de spin. --- Spin.

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Group theory --- Theory of relativity. Unified field theory --- Mathematical physics --- Lorentz transformations --- 530.1 --- Special relativity (Physics) --- Transformations (Mathematics) --- Basic principles of physics --- Lorentz transformations. --- 530.1 Basic principles of physics --- Lorentz groups --- Lorentz, Groupes de --- Lorentz groups. --- Groupes topologiques --- Lie, Groupes de --- Relativité générale (physique) --- Representation des groupes --- Application des groupes a la physique --- Application a la physique

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This book takes a fresh, systematic approach to determining the equation of motion for the classical model of the electron introduced by Lorentz 130 years ago. The original derivations of Lorentz, Abraham, Poincaré, and Schott are modified and generalized for the charged insulator model of the electron to obtain an equation of motion consistent with causal solutions to the Maxwell-Lorentz equations and the equations of special relativity. The solutions to the resulting equation of motion are free of pre-acceleration and pre-deceleration. The generalized method is applied to obtain the causal solution to the equation of motion of a charge accelerating in a uniform electric field for a finite time interval. Alternative derivations of the Landau-Lifshitz approximation are given as well as necessary and sufficient conditions for the Landau-Lifshitz approximation to be an accurate solution to the exact Lorentz-Abraham-Dirac equation of motion. Binding forces and a total stress-momentum-energy tensor are derived for the charged insulator model. Appendices provide simplified derivations of the self-force and power at arbitrary velocity. In this third edition, some of the history has been made more accurate and some of the derivations have been simplified and clarified. A detailed three-vector exact solution to the Landau-Lifshitz approximate equation of motion is given for the problem of an electron traveling in a counterpropagating plane-wave laser-beam pulse. Semi-classical analyses are used to derive the conditions that determine the significance of quantum effects not included in the classical equation of motion. The book is a valuable resource for students and researchers in physics, engineering, and the history of science.

Differential equations --- Mathematical physics --- Classical mechanics. Field theory --- Electromagnetism. Ferromagnetism --- Experimental nuclear and elementary particle physics --- differentiaalvergelijkingen --- deeltjesfysica --- elektrodynamica --- wiskunde --- fysica --- mechanica --- Lorentz transformations. --- Relativistic fluid dynamics. --- Electromagnetic theory.

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This thesis describes one of the most precise experimental tests of Lorentz symmetry in electrodynamics by light-speed anisotropy measurement with an asymmetric optical ring cavity. The author aims to answer the fundamental, hypothetical debate on Lorentz symmetry in the Universe. He concludes that the symmetry is protected within an error of 10-15, which means providing one of the most stringent upper limits on the violation of the Lorentz symmetry in the framework of the Standard Model Extension. It introduces the following three keys which play an important role in achieving high-precision measurement: (1) a high-index element (silicon) interpolated into part of the light paths in the optical ring cavity, which improves sensitivity to the violation of the Lorentz symmetry, (2) double-pass configuration of the interferometer, which suppresses environmental noises, and (3) continuous data acquisition by rotating the optical ring cavity, which makes it possible to search for higher-order violations of Lorentz symmetry. In addition to those well-described keys, a comprehensive summary from theoretical formulations to experimental design details, data acquisition, and data analysis helps the reader follow up the experiments precisely.

Physics. --- Gravitation. --- Observations, Astronomical. --- Astronomy --- Classical and Quantum Gravitation, Relativity Theory. --- Classical Electrodynamics. --- Astronomy, Observations and Techniques. --- Observations. --- Lorentz transformations. --- Special relativity (Physics) --- Ether drift --- Mass energy relations --- Relativity theory, Special --- Restricted theory of relativity --- Special theory of relativity --- Relativity (Physics) --- Transformations (Mathematics) --- Optics. --- Electrodynamics. --- Astronomy—Observations. --- Astronomical observations --- Observations, Astronomical --- Dynamics --- Physics --- Light --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties