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"This Element is a concise, high-level introduction to the philosophy of physical symmetry. It begins with the notion of physical representation (the kind of empirical representation of nature that we effect in doing physics), and then lays out the historically and conceptually central case of physical symmetry that frequently falls under the rubric of "the Relativity Principle", or "Galileo's Ship". This material is then used as a point of departure to explore the key hermeneutic challenge concerning physical symmetry in the last century, namely understanding the physical significance of the notion of "local" gauge symmetry. The approach taken stresses both the continuity with historically important themes such as the Relativity Principle, as well as novel insights earned by working with contemporary media such as the covariant phase space and derived critical locus formalisms"--

Symmetry.

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Symmetry --- Symmetry.

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Symmetry (biology) --- Symmetry (art)

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The Force of Symmetry gives an elementary introduction to the spectacular interplay between the three great themes of contemporary physics: quantum behaviour; relativity; and symmetry. In clear, non-technical language, though without oversimplification, it explores many fascinating aspects of modern physics, discussing the nature and interaction of force and matter. All these themes are drawn together, towards the end of the book, to describe the most successful physics theory in history, the 'standard model' of subatomic particles. The lively and non-technical approach of this book will make it suitable for first-year undergraduates in the physical sciences and mathematics, or even to those just about to embark on such courses. It will also be a valuable accompaniment to more advanced texts on quantum mechanics and particle physics.

Symmetry (Physics)

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Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.

Symmetry (Mathematics)