The Language of Symmetry in Physics
How do physicists use the mathematics of group theory?
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You have experienced the concept of symmetry even since you were young. We stare at a mirror and see ourselves. We might find subtle satisfaction in looking at a pattern that ‘repeats’ in some logical way. We might even smile shyly at a person on the bus with excellent symmetrical features. For most people, however, the word symmetry is associated with a mirror — a reflection. Whilst a reflection certainly is classed as a type of symmetry, there are many more types.
It turns out that symmetry itself plays a profound role in nature, and as such, physics. Different species of particles organise themselves in symmetric ways, but symmetry is also a mathematical explanation for conserved quantities like momentum and energy. Hell, there’s even a whole field of theoretical physics called ‘supersymmetry’.
Whilst I am not a professional mathematician (I have my friends for that), I found it imperative to get up to speed with the language of symmetry while taking my master’s in theoretical physics. So I wanted to write this post to look at some simple examples in physics and math on where we can apply group…
