Translational Symmetry

In geometry, a translation "slides" an object by a a: Ta(p) = p + a.

In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation. Discrete translational symmetry is invariance under discrete translation.

Analogously an operator A on functions is said to be translation invariant with respect to a translation operator if the result after applying A doesn't change if the argument function is translated. More precisely it must hold that

Laws of physics are translationally invariant if they do not distinguish different points in space. According to Noether's theorem, translational symmetry of a physical system is equivalent to the momentum conservation law.

Translational symmetry of an object means that a particular translation does not change the object. For a given object, the translations for which this applies form a group, the symmetry group of the object, or, if the object has more kinds of symmetry, a subgroup of the symmetry group

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Other articles related to "translational symmetry, symmetry":

Formal Treatment - Rotational Symmetry With Translational Symmetry
2-fold rotational symmetry together with single translational symmetry is one of the Frieze groups ... Together with double translational symmetry the rotation groups are the following wallpaper groups, with axes per primitive cell p2 (2222) 4×2-fold rotation group of a parallelogrammic, rectangular ... any lattice (every lattice is upside-down the same, but that does not apply for this symmetry) it is e.g ...
Glide Reflection
... In the case of glide reflection symmetry, the symmetry group of an object contains a glide reflection, and hence the group generated by it ... Example pattern with this symmetry group + + +++ +++ +++ + Frieze group nr ... Example pattern with this symmetry group + + + + + + + + + For any symmetry group containing some glide reflection symmetry, the translation vector of any ...
Fracton
... Phonons are the result of applying translational symmetry to the potential in a Schrödinger equation ... Fractal self-similarity can be thought of as a symmetry somewhat comparable to translational symmetry ... Translational symmetry is symmetry under displacement or change of position, and self-similarity is symmetry under change of scale ...
Lattice Points - Symmetry Considerations and Examples
... A lattice is the symmetry group of discrete translational symmetry in n directions ... A pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself ... the orbit of a group action under translational symmetry, is a translate of the translation lattice a coset, which need not contain the origin, and therefore need not be a lattice in the previous sense ...

Famous quotes containing the word symmetry:

    What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.
    George Gordon Noel Byron (1788–1824)