Special Relativity / Lecture Notes in Physics Bd.702 (PDF)
After a century of successes, physicists still feel the need to probe the limits of the validity of theories based on special relativity. Canonical approaches to quantum gravity, non-commutative geometry, string theory and unification scenarios predict...
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After a century of successes, physicists still feel the need to probe the limits of the validity of theories based on special relativity. Canonical approaches to quantum gravity, non-commutative geometry, string theory and unification scenarios predict tiny violations of Lorentz invariance at high energies.
The present book, based on a recent seminar devoted to such frontier problems, contains reviews of the foundations of special relativity and the implications of Poincaré invariance as well as comprehensive accounts of experimental results and proposed tests.
The book addresses, besides researchers in the field, everyone interested in the conceptual and empirical foundations of our knowledge about space, time and matter.
R. Bluhm
Colby College, Waterville, ME 04901, USA
rtbluhm@colby.edu
Abstract. The Standard Model Extension (SME) provides the most general observerindependent field theoretical framework for investigations of Lorentz violation. The SME lagrangian by definition contains all Lorentz-violating interaction terms that can be written as observer scalars and that involve particle fields in the Standard Model and gravitational fields in a generalized theory of gravity. This includes all possible terms that could arise from a process of spontaneous Lorentz violation in the context of a more fundamental theory, as well as terms that explicitly break Lorentz symmetry. An overview of the SME is presented, including its motivations and construction. Some of the theoretical issues arising in the case of spontaneous Lorentz violation are discussed, including the question of what happens to the Nambu-Goldstone modes when Lorentz symmetry is spontaneously violated and whether a Higgs mechanism can occur. A minimal version of the SME in flat Minkowski spacetime that maintains gauge invariance and power-counting renormalizability is used to search for leading-order signals of Lorentz violation. Recent Lorentz tests in QED systems are examined, including experiments with photons, particle and atomic experiments, proposed experiments in space, and experiments with a spin-polarized torsion pendulum.
1 Introduction
It has been 100 years since Einstein published his first papers on special relativity [1]. This theory is based on the principle of Lorentz invariance, that the laws of physics and the speed of light are the same in all inertial frames. A few years after Einsteins initial work, Minkowski showed that a new spacetime geometry emerges from special
The geometry is Riemannian, and the physics is invariant under general coordinate transformations. Lorentz symmetry, on the other hand, becomes a local symmetry. At each point on the spacetime manifold, local coordinate frames can be found in which the metric becomes the Minkowski metric. However, the choice of the local frame is not unique, and local Lorentz transformations provide the link between physically equivalent local frames.
The Standard Model (SM) of particle physics is a fully relativistic theory. The SM in Minkowski spacetime is invariant under global Lorentz transformations, whereas in a Riemannian spacetime the particle interactions must remain invariant under both general coordinate transformations and local Lorentz transformations. Particle fields are also invariant under gauge transformations. Exact symmetry under local gauge transformations leads to the existence of massless gauge fields, such as the photon. However, spontaneous breaking of local gauge symmetry in the electroweak theory involves the Higgs mechanism, in which the gauge fields can acquire a mass.
Classical gravitational interactions can be described in a form analogous to gauge theory by using a vierbein formalism [2]. This also permits a straightforward treatment of fermions in curved spacetimes. Covariant derivatives of tensors in the local Lorentz frame involve introducing the spin connection.
- Autoren: Jürgen Ehlers , Claus Lämmerzahl
- 2006, 2006, 533 Seiten, Englisch
- Herausgegeben: Jürgen Ehlers, Claus Lämmerzahl
- Verlag: Springer-Verlag GmbH
- ISBN-10: 354034523X
- ISBN-13: 9783540345237
- Erscheinungsdatum: 11.09.2006
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Größe: 19 MB
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From the reviews:
"In the last decade and a half, many scientists have come to believe that special relativity, as Einstein formulated it, will need to be modified to accommodate a quantum theory of gravity. … the volume presents an excellent survey of current research on Lorentz symmetry. Most of the book should be accessible to graduate students and researchers who are interested in the field … . provide abundant references, which should be quite valuable in a field with as many counterintuitive features as Lorentz violation research." (Brett D Altschul, Classical and Quantum Gravity, Vol. 24, 2007)
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