What is a Group?

Rationalising The Universe

Good morning RTU followers. Today I want give you a very brief introduction to an integral part of Theoretical Physics – Group Theory. When studying for my MSc I knew I had to get my head around this subject which to me initially seemed very dry and written in very purely mathematical language (i.e. not easy to read!) However once I’d dedicated some time the beauty of group theory began to fall into place – it’s a slow burner. The purpose of group theory is to classify and understand symmetries in the natural world. So without further ado let me lay down the principles of group theory as clearly as I can.

Firstly a group, denoted G, is a collection of elements call them g(1), g(2), g(3)…. and there exists a group operation, denote it *, which determines how the elements act on each other. Now the elements of the…

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