Standard-Model Extension

Standard-Model Extension (SME) is an effective field theory that contains the Standard Model, general relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework. CPT violation implies the breaking of Lorentz symmetry,and the SME includes operators that both break and preserve CPT symmetry. Standard-Model Extension (SME) is an effective field theory that contains the Standard Model, general relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework. CPT violation implies the breaking of Lorentz symmetry,and the SME includes operators that both break and preserve CPT symmetry. In 1989, Alan Kostelecký and Stuart Samuel proved that interactions in string theories could lead to the spontaneous breaking of Lorentz symmetry. Later studies have indicated that loop-quantum gravity, non-commutative field theories, brane-world scenarios, and random dynamics models also involve the breakdown of Lorentz invariance. Interest in Lorentz violation has grown rapidly in the last decades because it can arise in these and other candidate theories for quantum gravity. In the early 1990s, it was shown in the context of bosonic superstrings that string interactions can also spontaneously break CPT symmetry. This worksuggested that experiments with kaon interferometry would be promising for seeking possible signals of CPT violation due to their high sensitivity. The SME was conceived to facilitate experimental investigations of Lorentz and CPT symmetry, given the theoretical motivation for violation of these symmetries. An initial step, in 1995, was the introduction of effective interactions.Although Lorentz-breaking interactions are motivated by constructs such as string theory, the low-energy effective action appearing in the SME is independent of the underlying theory. Each term in the effective theory involves the expectation of a tensor field in the underlying theory. These coefficients are small due to Planck-scale suppression, and in principle are measurable in experiments. The first case considered the mixing of neutral mesons, because their interferometric nature makes them highly sensitive to suppressed effects. In 1997 and 1998, two papers by Don Colladay and Alan Kostelecký gave birth to the minimal SME in flat spacetime. This provided a framework for Lorentz violation across the spectrum of standard-model particles, and provided information about types of signals for potential new experimental searches. In 2004, the leading Lorentz-breaking terms in curved spacetimes were published,thereby completing the picture for the minimal SME. In 1999, Sidney Coleman and Sheldon Glashow presented a specialisotropic limit of the SME.Higher-order Lorentz violating terms have been studied in various contexts, including electrodynamics. The distinction between particle and observer transformations is essential to understanding Lorentz violation in physics because Lorentz violation implies a measurable difference between two systems differing only by a particle Lorentz transformation. In special relativity, observer Lorentz transformations relate measurements made in reference frames with differing velocities and orientations. The coordinates in the one system are related to those in the other by an observer Lorentz transformation—a rotation, a boost, or a combination of both. Each observer will agree on the laws of physics, since this transformation is simply a change of coordinates. On the other hand, identical experiments can be rotated or boosted relative to each other, while being studied by the same inertial observer. These transformations are called particle transformations, because the matter and fields of the experiment are physically transformed into the new configuration.