Breaking Lorentz Symmetry in Quantum Field Theory

Abstract

Symmetry under the Lorentz group is a fundamental assumption of virtually any fundamental theory used to describe elementary particle physics. For instance, the standard model as well as many extensions including supersymmetry and grand unified theories preserve Lorentz symmetry. Under very mild assumptions, the postulates of a point particle theory that preserves Lorentz invariance lead to the conclusion that CPT is preserved [1]. In this talk, I will discuss the construction of quantum field theories that break Lorentz and CPT symmetry. There are both experimental and theoretical motivations to develop such theories. Many sensitive experimental tests of Lorentz and CPT symmetry have been performed. For example, high precision tests involving atomic systems [2, 3], clock comparisons [4], and neutral meson oscillations [5] provide stringent tests of Lorentz and CPT symmetry. In the past, each such experiment has bounded phenomenological parameters that lack a clear connection with the microscopic physics of the standard model. It is desirable to have a single theory within the context of conventional quantum field theory and the standard model that could relate various experiments and be used to motivate future investigations. On the theoretical side, low-energy remnant effects that violate fundamental symmetries may arise in theories underlying the standard model. One example is string theory in which nontrivial structure of the vacuum solutions may induce observable Lorentz and CPT violations [6, 7, 8]. Terms involving standard model fields that violate Lorentz and CPT symmetry are assumed to arise from a general spontaneous symmetry breaking mechanism in which vacuum expectation values for tensor fields are generated in the underlying theory [9].