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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. Symmetric difference - Wikipedia

    en.wikipedia.org/wiki/Symmetric_difference

    Venn diagram of = . The symmetric difference is equivalent to the union of both relative complements, that is: [1] = (), The symmetric difference can also be expressed using the XOR operation ⊕ on the predicates describing the two sets in set-builder notation:

  4. Symmetry - Wikipedia

    en.wikipedia.org/wiki/Symmetry

    Upon this inherently symmetrical starting point, potters from ancient times onwards have added patterns that modify the rotational symmetry to achieve visual objectives. Cast metal vessels lacked the inherent rotational symmetry of wheel-made pottery, but otherwise provided a similar opportunity to decorate their surfaces with patterns pleasing ...

  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, ...

  6. Representation theory of the symmetric group - Wikipedia

    en.wikipedia.org/wiki/Representation_theory_of...

    The dimension of the representation that corresponds to the Young diagram is given by the hook length formula. To each irreducible representation ρ we can associate an irreducible character, χ ρ . To compute χ ρ (π) where π is a permutation, one can use the combinatorial Murnaghan–Nakayama rule . [ 3 ]

  7. Symmetry (physics) - Wikipedia

    en.wikipedia.org/wiki/Symmetry_(physics)

    The above ideas lead to the useful idea of invariance when discussing observed physical symmetry; this can be applied to symmetries in forces as well.. For example, an electric field due to an electrically charged wire of infinite length is said to exhibit cylindrical symmetry, because the electric field strength at a given distance r from the wire will have the same magnitude at each point on ...

  8. 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 ...

  9. 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