Abstract
Symmetry and group theory throughout physics
Highlights
As noticed in 1884 by Pierre Curie [1], physical properties of matter are tightly related to the kind of symmetry of the medium
These are examples of the considerable simplification brought by symmetry in physical problems
The symmetries introduced by elementary particle theorists are not so natural as those generally used in condensed matter physics
Summary
Life is possible on the Earth because of the physical properties of the molecules around us: O2, N2, H2O. O2 and N2 molecules are symmetric with respect to their center (Fig. 1) This implies that their electric dipole moment is zero. Oxygen and nitrogen do not contribute to the greenhouse effect This is an essential result, its proof is elementary. Its electronic structure has a remarkable property, namely the conduction band and the valence band are separated, except for a discrete set of points of the reciprocal space, where they touch This is in contrast with the situation in a metal or an insulator or semiconductor. In Appendix A this is shown to result from symmetry These are examples of the considerable simplification brought by symmetry in physical problems. We shall try to find the right compromise between too superficial and too technical considerations
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