Discrete Symmetry Transformations

Abstract

In Sect. 4.3 we have studied the transformation properties of quantum fields. The discussion was devoted to continuous transformations that can be constructed by starting from infinitesimal transformations “close to unity”. If a theory is invariant under such a transformation it will possess a Noether current and thus there will be a conservation law. In addition, however, there is the class of discrete symmetries, which have to be described differently. Discrete symmetries can be employed to relate the behavior of different physical systems, for example, those that differ by an interchange of particles and antiparticles. New conserved quantities (e.g., parity, charge parity) and selection rules can be generated by discrete symmetries. We will study three types of discrete transformations which are of fundamental importance: space inversion \(\hat P\), charge conjugation Ĉ, and time reversal \(\hat T\). All noninteracting field theories are invariant under these transformations but this will change if interactions are present that break the symmetry. A prominent example for this is the famous maximal violation of space inversion symmetry (parity) in weak interactions. Also the time-reversal symmetry is (very slightly) violated in nature as witnessed by the decay of the \({K^0}/{\bar K^0}\) mesons.