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  2. Symmetry in quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics

    In quantum electrodynamics, the local symmetry group is U(1) and is abelian. In quantum chromodynamics, the local symmetry group is SU(3) and is non-abelian. The electromagnetic interaction is mediated by photons, which have no electric charge. The electromagnetic tensor has an electromagnetic four-potential field possessing gauge symmetry.

  3. SYZ conjecture - Wikipedia

    en.wikipedia.org/wiki/SYZ_conjecture

    Along with the homological mirror symmetry conjecture, it is one of the most explored tools applied to understand mirror symmetry in mathematical terms. While the homological mirror symmetry is based on homological algebra, the SYZ conjecture is a geometrical realization of mirror symmetry.

  4. Hermann–Mauguin notation - Wikipedia

    en.wikipedia.org/wiki/Hermann–Mauguin_notation

    Hermann–Mauguin symbols show non-equivalent axes and planes in a symmetrical fashion. The direction of a symmetry element corresponds to its position in the Hermann–Mauguin symbol. If a rotation axis n and a mirror plane m have the same direction, then they are denoted as a fraction ⁠ n / m ⁠ or n /m.

  5. Diagram (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Diagram_(mathematical_logic)

    In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.

  6. Symmetry in mathematics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_mathematics

    Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object

  7. Particle physics and representation theory - Wikipedia

    en.wikipedia.org/wiki/Particle_physics_and...

    Isospin symmetry can be generalized to flavour symmetry, an SU(3) group corresponding to the similarity between up quarks, down quarks, and strange quarks. [7] This is, again, an approximate symmetry, violated by quark mass differences and electroweak interactions—in fact, it is a poorer approximation than isospin, because of the strange ...

  8. Symmetry element - Wikipedia

    en.wikipedia.org/wiki/Symmetry_element

    The elements of this symmetry group should not be confused with the "symmetry element" itself. Loosely, a symmetry element is the geometric set of fixed points of a symmetry operation. For example, for rotation about an axis, the points on the axis do not move and in a reflection the points that remain unchanged make up a plane of symmetry.

  9. Symmetry operation - Wikipedia

    en.wikipedia.org/wiki/Symmetry_operation

    In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out. For example, a 1 ⁄ 3 turn rotation of a regular triangle about its center, a reflection of a square across its diagonal, a translation of the Euclidean plane, or a point reflection of a sphere through its center are all symmetry operations.

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