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
Sphere symmetrical group o representing an octahedral rotational symmetry. The yellow region shows the fundamental domain. Symmetry (from Greek συμμετρεῖν symmetreín "to measure together") has two meanings. The first is a vague sense of harmonious and beautiful proportion and balance. 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. Symmetry
List of cycles List of cycles
In mathematics, especially in geometry and group theory, a lattice in Lattice (group)
Tessellation Ceramic Tiles in Marrakech, forming edge-to-edge, regular and other tessellations Some special kinds of tessellations include regular, with tiles all of the same shape; semi-regular, with tiles of more than one shape; and aperiodic tilings, which use tiles that cannot form a repeating pattern.
Generally speaking, an object with rotational symmetry, also known in biological contexts as radial 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". 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: This usage of the term covariant should not be confused with the related concept of a covariant vector. On manifolds, the words covariant and contravariant refer to how objects transform under general coordinate transformations. Confusingly, both covariant and contravariant four-vectors can be Lorentz covariant quantities. Local Lorentz covariance, which follows from general relativity, refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point.