Search results
Results From The WOW.Com Content Network
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 ...
Note that this article refers to O(1, 3) as the "Lorentz group", SO(1, 3) as the "proper Lorentz group", and SO + (1, 3) as the "restricted Lorentz group". Many authors (especially in physics) use the name "Lorentz group" for SO(1, 3) (or sometimes even SO + (1, 3)) rather than O(1, 3). When reading such authors it is important to keep clear ...
The Poincaré group, named after Henri Poincaré (1905), [1] was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. [2] [3] It is a ten-dimensional non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics.
[nb 1] This group is significant because special relativity together with quantum mechanics are the two physical theories that are most thoroughly established, [nb 2] and the conjunction of these two theories is the study of the infinite-dimensional unitary representations of the Lorentz group. These have both historical importance in ...
The spacetime symmetry group for special relativity is the Poincaré group, which is a ten-dimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is logical to ask what symmetries, if any, might apply in General Relativity.
Lie groups – Group that is also a differentiable manifold with group operations that are smooth; Lorentz group – Lie group of Lorentz transformations; Poincaré group – Group of flat spacetime symmetries; Bondi–Metzner–Sachs group – Asymptotic symmetry group of General Relativity
The indefinite orthogonal group O(1,n), also called the (n+1)-dimensional Lorentz group, is the Lie group of real (n+1)×(n+1) matrices which preserve the Minkowski bilinear form. In a different language, it is the group of linear isometries of the Minkowski space. In particular, this group preserves the hyperboloid S.
Foundational issues. principle of relativity; speed of light; faster-than-light; biquaternion; conjugate diameters; four-vector. four-acceleration; four-force