Symmetry arguments and the totalitarian principle in the physics of liquid crystals and other condensed matter systems

Abstract

ABSTRACTSymmetry arguments constitute one of the most powerful tools of physics. As shown by Emmy Noether, continuous symmetries correspond to physical conservation laws. In analogy with dimensional arguments, symmetry arguments can also be used to predict the behaviour of physical systems. Mistaking symmetries, on the other hand, can lead to grave errors. In this paper, we describe and give examples of certain types of symmetry arguments which can be useful in general and, in particular, in the field of liquid crystals. In using symmetry arguments to predict physical phenomena, the totalitarian principle, made popular by Murray Gell-Mann, is often used, either explicitly or implicitly. We discuss the totalitarian principle, its origins, history and philosophical implications. Our goal is to outline a simple symmetry-based procedure which may be useful in gaining insights into and describing the behaviour of complex physical systems such as liquid crystals.