They conjectured that the laws of physics are invariant under the symmetry group of de Sitter space (maximally symmetric space-time), rather than the Poincare group of special relativity.
The Poincare group "contracts" to the Galilean group for low velocities.
Analogously the de Sitter group "contracts" to the Poincare group for short distance kinematics, when the order of magnitude of all translations are small compared to the de Sitter radius.
Extension of the algebra of Poincare group
generators and violation of P invariance.
The 10-parameter Poincare group
is the semi-direct product of the 6-parameter Lorentz group with the 4-parameter group of space-time translations.
The 11 papers in this collection review the role of nontrivial symmetries in equilibrium thermodynamics, the Lie derivative of spinor fields, Landen transformation formulas for Jacobi elliptic functions, and the quantum electrodynamics of the Poincare group
Auyang follows some influential authors in claiming that the Poincare group
is needed if one wants to allow for torsion in the spacetime manifold.
The fifth section examines results obtained from Wigner's classification of the irreducible representations of the Poincare group.
The profound significance of Wigner's analysis of the irreducible representations of the Poincare group (see ; , pp.
A result of this analysis is that a system that is stable for a long enough period of time is a basis for an irreducible representation of the Poincare group (see , pp.
Three well known mathematical structures are used here: the variational principle, Wigner's analysis of the irreducible representations of the Poincare group and duality transformations of electromagnetic fields.
It is known that the Poincare group
is the Wigner-Inonu group contraction of the de Sitter Group SO(4,1) after taking the throat size r = [infinity].