continuous translational symmetry is the invariance of a system of equations under any translation (without rotation). Discrete translational symmetry is invariant...

about all points implies translational symmetry with respect to all translations, so space is homogeneous, and the symmetry group is the whole E(m). With...

Time-translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a...

Group Periodic function Shift operator Symmetries in quantum mechanics Time translation symmetry Translational symmetry Lecture notes by Robert Littlejohn...

that looks the same before and after translation is said to have translational symmetry. A common example is a periodic function, which is an eigenfunction...

lattice is the symmetry group of discrete translational symmetry in n directions. A pattern with this lattice of translational symmetry cannot have more...

crystal ground state, the continuous translational symmetry in space is broken and replaced by the lower discrete symmetry of the periodic crystal. As the...

the translational symmetry of the crystal. The three dimensions of space afford 14 distinct Bravais lattices describing the translational symmetry. All...

translational symmetry with respect to all translations (because translations are compositions of rotations about distinct points), and the symmetry group...

the same probability distribution, the observable has translational symmetry. Spontaneous symmetry breaking occurs when this relation breaks down, while...

pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction...

belong to a different space group than the crystal of the solid. High-symmetry points in the Brillouin zone belong to different point-group representations...

lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself. In the 5 cases of rotational symmetry of order 3...

corresponding glide-reflection symmetry reduces to a combination of reflection symmetry and translational symmetry. Glide-reflection symmetry with respect to two...

symmetry, but with respect to different axes. two 2D patterns have translational symmetry, each in one direction; the two translation vectors have the same...

despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named...

rotational symmetry if the object can be rotated about a fixed point (or in 3D about a line) without changing the overall shape. An object has translational symmetry...

the Lorentz and rotational symmetries) and P is a general vector (giving the translational symmetries). Other symmetries affect multiple fields simultaneously...

relativity. It is an expression of one of the fundamental symmetries of space and time: translational symmetry. Advanced formulations of classical mechanics, Lagrangian...

discrete translational symmetry. In order to model and study such a periodic system, one needs a mathematical "handle" to describe the symmetry and hence...

in which case these symmetry groups can be ignored. Cn and Dn for n = 1, 2, 3, 4, and 6 can be combined with translational symmetry, sometimes in more...

lattice's symmetry category is wallpaper group p4m. A pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than...

crystallography, there is additional translational symmetry, and point groups are not enough to describe the full symmetry of crystals, so the full space group...

the continuous translational symmetry of time implies the conservation of energy Space and momentum - the continuous translational symmetry of space implies...

diagonal axes. dihedral symmetry. In addition, groups of clues can display other types of symmetry, such as translational symmetry. Also refer to automorphic...

the translational symmetry as [∞]+, or Coxeter-Dynkin diagram as the composite of two reflections. For a pattern without translational symmetry there...

because it can easily be used to include translational symmetry elements, and it specifies the directions of the symmetry axes. Rotation axes are denoted by...

and rotation symmetries) and translational symmetries. Thus, lattices can be categorized based on what point group or translational symmetry applies to...

conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time. In 1843, James...

dihedral symmetry (a 90° rotational symmetry, which also includes a symmetry on both orthogonal axis, 180° rotational symmetry, and diagonal symmetry) is known...