The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It is...

theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group nor a semisimple group. It is fundamental...

manifold Poincaré duality Poincaré disk model Poincaré expansion Poincaré gauge Poincaré group Poincaré half-plane model Poincaré homology sphere Poincaré inequality...

the theory of discrete groups that had developed in the theory of modular forms, in the hands of Felix Klein and Henri Poincaré. The initial application...

Henri Poincaré in 1904, the theorem concerns spaces that locally look like ordinary three-dimensional space but which are finite in extent. Poincaré hypothesized...

general group. Lie groups appear in symmetry groups in geometry, and also in the Standard Model of particle physics. The Poincaré group is a Lie group consisting...

Lorentz transformations and Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean...

with 1 ≤ p ≤ n. The lemma was introduced by Henri Poincaré in 1886. Especially in calculus, the Poincaré lemma also says that every closed 1-form on a simply...

the Wightman axioms is that there is a Hilbert space, upon which the Poincaré group acts unitarily. In this way, the concepts of energy, momentum, angular...

is described in special relativity by a group of transformations of the spacetime known as the Poincaré group. Another important example is the invariance...

linear group: for instance, the special affine group is the subgroup defined by the semidirect product, SL(n, F) ⋉ Fn, and the Poincaré group is the affine...

the form of the Poincaré quantum group. There were also claims based on an earlier κ {\displaystyle \kappa } -Poincaré quantum group introduced by Jurek...

isometry group of the Poincaré half-plane model of the hyperbolic plane is PSL(2,R). The isometry group of Minkowski space is the Poincaré group. Riemannian...

Sitter algebra to the super-Poincaré algebra as the AdS radius diverges R → ∞; or the Poincaré group to the Galilei group, as the speed of light diverges:...

In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions...

mathematics, the κ-Poincaré group, named after Henri Poincaré, is a quantum group, obtained by deformation of the Poincaré group into a Hopf algebra...

the same class. Fixed points of isometry groups in Euclidean space Euclidean plane isometry Poincaré group Coordinate rotations and reflections Reflection...

representations of the Poincaré group which have either finite or zero mass eigenvalues. (These unitary representations are infinite-dimensional; the group is not semisimple...

the same manner as special relativity. The Lorentz group is a subgroup of the Poincaré group—the group of all isometries of Minkowski spacetime. Lorentz...

The BMS group also has a similar structure as the Poincaré group: just as the Poincaré group is a semidirect product between the Lorentz group and the...

of transformations that also includes translations is known as the Poincaré group. Many physicists—including Woldemar Voigt, George FitzGerald, Joseph...

mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted Sp(2n, F) and Sp(n) for...

Examples of the use of groups in physics include the Standard Model, gauge theory, the Lorentz group, and the Poincaré group. Group theory can be used to...

excitation of a field A particle is an irreducible representation of the Poincaré group A particle is an observed thing Subatomic particles are either "elementary"...

point. There is a generalization of this concept to cover Poincaré covariance and Poincaré invariance. In general, the (transformational) nature of a...

after Henri Poincaré: Euler–Poincaré characteristic Hilbert–Poincaré series Poincaré–Bendixson theorem Poincaré–Birkhoff theorem Poincaré–Birkhoff–Witt...

group generated by the orthogonal reflections. The Poincaré group is the affine group of the Lorentz group O(1,3): R 1 , 3 ⋊ O ⁡ ( 1 , 3 ) {\displaystyle...

called quantum fields which form covariant representations of the Poincaré group. The group of space-time translations is commutative, and so the operators...

unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation of matrix multiplication. The unitary group is a...

algebra Gamma matrices Lorentz group Möbius transformation Poincaré group Representation theory of the Poincaré group Symmetry in quantum mechanics Wigner's...