ABSTRACT

This chapter discusses the very basic foundations of symmetry arguments, how transformations of time, space, and other properties may be described within the group theory language, and how it may help us confront different physical situations. Symmetries play a central role in modern physics and the mathematical language for describing them is found in group theory. Invoking symmetry arguments can aid us in analysing and making simplifying statements regarding many physical systems. An important aspect of symmetries is that if two different transformations are both symmetries of a physical system, then also their composition is a symmetry. In physics, it is very common that a system is not completely symmetric under the full set of possible transformations, but only under a subset. Symmetries can often help in reducing the complexity of a given problem and help us argue why a solution must have a particular form. Any combination of such translations and rotations are also symmetries of the current density.