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...

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...

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

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

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 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...

the Poincaré group, Bargmann's theorem applies. (See Wigner's classification of the representations of the universal cover of the Poincaré group.) The...

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

mentioned) and the Poincaré group. The latter case is important to Wigner's classification of the projective representations of the Poincaré group, with applications...

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

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...

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

subsequent enlargement of the group for a theory based on a narrower group." The Poincaré group, the transformation group of special relativity, being...

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

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

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

\operatorname {SL} (n,F)\ltimes F^{n}} , and the Poincaré group is the affine group associated to the Lorentz group, O ⁡ ( 1 , 3 , F ) ⋉ F n {\displaystyle \operatorname...

{A}}(O_{2})]=0} . Poincaré covariance: A strongly continuous unitary representation U ( P ) {\displaystyle U({\mathcal {P}})} of the Poincaré group P {\displaystyle...

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...

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...

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...

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...

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

of transformations that also includes translations is known as the Poincaré group where initial time and initial origin coordinates of the two reference...

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:...

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

Representation theory of the Poincaré group Wigner's classification Pauli–Lubanski pseudovector Representation theory of the diffeomorphism group Rotation operator...

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...