Search results
Results from the WOW.Com Content Network
Poincaré symmetry is the full symmetry of special relativity. It includes: translations (displacements) in time and space, forming the abelian Lie group of spacetime translations (P); rotations in space, forming the non-abelian Lie group of three-dimensional rotations (J); boosts, transformations connecting two uniformly moving bodies (K).
In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type. Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions:
Physical problems are often investigated and solved by noticing features which have some form of symmetry. For example, in the Schwarzschild solution, the role of spherical symmetry is important in deriving the Schwarzschild solution and deducing the physical consequences of this symmetry (such as the nonexistence of gravitational radiation in a spherically pulsating star).
A space group is called symmorphic (or split) if there is a point such that all symmetries are the product of a symmetry fixing this point and a translation. Equivalently, a space group is symmorphic if it is a semidirect product of its point group with its translation subgroup. There are 73 symmorphic space groups, with exactly one in each ...
To give some context for the general reader, the naive expectation for asymptotically flat spacetime symmetries, i.e., symmetries of spacetime seen by observers located far away from all sources of the gravitational field, would be to extend and reproduce the symmetries of flat spacetime of special relativity, viz., the Poincaré group, also called the inhomogeneous Lorentz group, [2] which is ...
The group depends only on the dimension n of the space, and is commonly denoted E(n) or ISO(n), for inhomogeneous special orthogonal group. The Euclidean group E( n ) comprises all translations , rotations , and reflections of E n {\displaystyle \mathbb {E} ^{n}} ; and arbitrary finite combinations of them.
This means that the symmetry group of space time is a de Sitter group rather than the Poincaré group. This results in spacetime being slightly curved even in the absence of matter or energy. This residual curvature is caused by a cosmological constant to be determined by observation.
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object.