The concept of symmetry plays a central role in our understanding of the fundamental laws of Nature. Through a deep mathematical theorem due to A.E. Noether, all conservation laws of classical physics are related to symmetries. In this chapter we start from the intuitively obvious notions of translation and rotation symmetries which are part of the axioms of Euclidian geometry. Following W. Heisenberg, we introduce the idea of isospin as a first example of an internal symmetry. A further abstraction leads to the concept of a global versus local, or gauge symmetry, which is a fundamental property of General Relativity. Combining the notions of internal and gauge symmetries we obtain the Yang-Mills theory which describes all fundamental interactions among elementary particles. A more technical part, which relates a gauge symmetry of the Schrödinger equation of quantum mechanics to the electromagnetic interactions, is presented in a separate section and its understanding is not required for the rest of the book.
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