Overview of the Standard Model Extension: Implications and Phenomenology of Lorentz Violation

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.

Lorentz-violating Euler-Heisenberg effective action

“…The effective theory used in these analyses was mainly the Lorentz-violating QED [13], a subset of the minimal standard-model extension [4,5]. For an overview and references on this extended QED, see the review [14] and the incomplete list of works [15][16][17][18][19][20][21][22].…”

CPT and Lorentz violation effects in hydrogenlike atoms

“…In the former paper, a nonrelativistic Hamiltonian for a free electron was obtained using the Foldy-Wouthysen method (1/m e -series), within the first order approximation with respect to all possible SME-corrections in the fermion sector of extended QED [1,2]. In the special case of the axial vector background b µ , the resulting nonrelativistic Hamiltonian can be obtained from the formulas of paper [25]:…”

“…For the b µ coupling, the calculations performed have led to the Pauli Hamiltonian of the form (3.27). The contributions in the fermion Lagrangian and Hamiltonian, corresponding to a µ coupling, are as follows [1,2]:…”

“…It is an effective theory (applicable at the energies E ≪ E Pl ) formulated axiomatically as a set of corrections to the Lagrangian of the Standard Model fulfilling some 'natural' requirements [1,2] such as observer Lorentz invariance, 4-momentum conservation, unitarity, and microcausality. In what follows, we will focus on a subset of the SME referred to as the minimal SME in flat Minkowsky spacetime that also requires local SU (3) C × SU (2) I × U (1) Y gauge invariance and power-counting renormalizability.…”

Low energy tests of gravitational and quantum mechanical principles

“…In this context, the so-called standard model extension (SME) [1,2] could be considered one of the most general approaches including Lorentz violations, and the deformed dispersion relation to be considered in the present work is just one possibility [1].…”