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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.
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.
This book contains the Proceedings of the Ninth Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington May 17-26, 2022. The Meeting focused on tests of these fundamental symmetries and on related theoretical issues, including scenarios for possible violations. Experimental topics covered at the meeting include astrophysical observations of neutrinos, photons, cosmic rays, pulsars, and gravitational waves; investigations at accelerators and storage rings involving neutral mesons, muons, quarks, and flavor-changing processes; gravity tests in the laboratory and in the solar system; spectroscopic studies of ions, atoms, molecules, and exotic atoms; measurements involving spin motion; comparative tests between matter and antimatter; lasers and masers; measurements involving neutrons; investigations with cavities, oscillators, and resonators; neutrino oscillations, propagation, and endpoint measurements.Theoretical and phenomenological topics discussed involved the identification of signatures for CPT and Lorentz violation in particle physics, electromagnetism, and gravity; mechanisms and toy models for spacetime-symmetry breakdown; studies in field theory, gravitation, and particle physics; and condensed-matter applications.
This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.
This book reviews various modified gravity models, including those with modifications in the pure gravitational sector; those involving extra fields, that is, scalar-tensor and vector-tensor gravity theories; gravity models with Lorentz symmetry breaking; and nonlocal gravity models. The authors discuss both classical and quantum aspects of these theories. The book is unique in bringing together all the current alternatives to Einstein gravity in one source and serves as an excellent starting point for graduate students and other newcomers seeking an overview.
This proceedings volume records the advances in quantum beam physics since the first meeting in Monterey (1998). In addition to further progress regarding quantum effects in beam dynamics, photon-electron interaction in beam handling, beam phenomena under strong fields, and quantum methodologies in beam physics, the newly introduced topics ? the physics of condensed beams as well as astro-beam physics and laboratory astrophysics ? have also been well documented by world experts in the field.This book should be a valuable reference to those who are interested in the joint frontiers of beam physics and other fields such as astrophysics and condensed matter physics.
This book contains the Proceedings of the Sixth Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington on June 17-21, 2013. The Meeting focused on tests of these fundamental symmetries and on related theoretical issues, including scenarios for possible violations.Topics covered at the meeting include searches for CPT and Lorentz violations involving: accelerator and collider experiments; atomic, nuclear, and particle decays; birefringence, dispersion, and anisotropy in cosmological sources; clock-comparison measurements; electromagnetic resonant cavities and lasers; tests of the equivalence principle; gauge and Higgs particles; high-energy astrophysical observations; laboratory tests of gravity; matter interferometry; neutrino oscillations and propagation; oscillations and decays of neutral mesons; particle-antiparticle comparisons; post-newtonian gravity in the solar system and beyond; second- and third-generation particles; space-based missions; spectroscopy of hydrogen and antihydrogen; spin-polarized matter; and time-of-flight measurements. Theoretical discussions include physical effects at the level of the Standard Model, General Relativity, and beyond; the possible origins and mechanisms for Lorentz and CPT violations; classical and quantum issues in field theory, particle physics, gravity, and string theory; and mathematical foundations including Finsler geometry.
This book reviews various modified gravity models, including those with modifications in the pure gravitational sector; those involving extra fields, that is, scalar-tensor and vector-tensor gravity theories; gravity models with Lorentz symmetry breaking; and nonlocal gravity models. The authors discuss both classical and quantum aspects of these theories. The book is unique in bringing together all the current alternatives to Einstein gravity in one source and serves as an excellent starting point for graduate students and other newcomers seeking an overview. This second edition has been expanded with new results from a variety of approaches including f(R,Q,P) gravity, galileon gravity and massive gravity. Extended discussions of Lorentz-breaking terms and of non-local field theory have been added and a completely new chapter is devoted to models based on non-Riemannian geometry.
The relativistic string theory was born in 1960s. The stimulus was an observation that the dual model of hadronic interactions proposed by Veneziano is adequate not to the quantum theory of usual (null-dimensional) particles but to the theory of one-dimensional relativistic objects -- the strings. It has been immediately found that a self-consistent quantum theory of (bosonic) relativistic strings can be constructed in frames of standard quantisation scheme only in a space-time of dimension 26. Inclusion of fermions has decreased this critical dimension to 10. However, it is evident from the experiment, that elementary particles and their constituents 'live' in the space-time of dimension 4. The attempt to show that extra 6 dimensions are compactified on the scale of Planck's length, in the spirit of old ideas by Kaluza-Klein, just created further complications. This book differs from traditional presentations of the classical and quantum theory of relativistic strings by two aspects. First, it proposes and consistently implements an idea of mathematical modelling and computer visualisation of topologically non-trivial solutions of the classical equations of motion of relativistic strings. Second, on this basis it successfully implements a quantisation scheme, originating from the papers by G P Pron'ko, which uses a different set of dynamical variables, canonically equivalent to the variables of standard scheme, in frames of Hamiltonian formalism and Dirac's quantisation procedure.
This textbook presents a detailed introduction to the general concepts of quantum field theory, with special emphasis on principal aspects of functional methods and renormalization in gauge theories, and includes an introduction to semiclassical and perturbative quantum gravity in flat and curved spacetimes.