Symmetry
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We’ve been discussing the Higgs (its interactions , its role in particle mass , and its vacuum expectation value ) as part of our ongoing series on understanding the Standard Model with Feynman diagrams .
Quantum Diaries
Symmetry (from Greek συμμετρεῖν symmetreín "to measure together") has two meanings. The first is a vague sense of harmonious and beautiful proportion and balance. [ 1 ] [ 2 ] The second is an exact mathematical "patterned self-similarity" that can be demonstrated with the rules of a formal system , such as geometry or physics . Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together. [ 2 ] [ 3 ] Mathematical symmetry may be observed
Symmetry
Tessellation
Ceramic Tiles in Marrakech , forming edge-to-edge, regular and other tessellations Tessellation is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps.
Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation . An object may have more than one rotational symmetry ; for instance, if reflections or turning it over are not counted. The degree of rotational symmetry is how many degrees the shape has to be turned to look the same on a different side or vertex.
Rotational symmetry
Lorentz covariance
In physics , Lorentz symmetry , named for Hendrik Lorentz , is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space". [ 1 ] Lorentz covariance , a related concept, is a key property of spacetime following from the special theory of relativity . Lorentz covariance has two distinct, but closely related meanings: A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group . According to the representation theory of the Lorentz group, these quantities are built out of scalars , four-vectors , four-tensors , and spinors . In particular, a scalar (e.g. the space-time interval ) remains the same under Lorentz transformations and is said to be a "Lorentz invariant" (i.e. they transform under the trivial representation ).