- #1

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- Summary:
- The restricted Lorentz group

The full Lorentz group includes discontinuous transformations, i.e., time inversion and space inversion, which characterize the non-orthochronous and improper Lorentz groups, respectively. However, these groups are excluded from the Poincare group, in which only the proper, orthochronous Lorentz group is included. From my understanding, the exclusion of the discontinuous Lorentz transformations is necessary for the Poincare group to be considered a Lie Group with a Lie algebra as represented by the generators.

My question is two-fold: 1) Is my understanding correct that the exclusion of the discontinuous Lorentz transformations from the Poincare group is done so that the Poincare group can be represented as generators of a Lie algebra? 2) Do other distinct reasons exist for excluding the discontinuous Lorentz transformations from the Poincare group?

My question is two-fold: 1) Is my understanding correct that the exclusion of the discontinuous Lorentz transformations from the Poincare group is done so that the Poincare group can be represented as generators of a Lie algebra? 2) Do other distinct reasons exist for excluding the discontinuous Lorentz transformations from the Poincare group?