Retrieving "Infinitesimal Generator" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Identity Transformation

   Linked via "infinitesimal generators"

   Relation to Infinitesimal Generators
   Transformations close to the identity in continuous groups are generated by infinitesimal generators. For the Lorentz Group, the generators $G_{\mu\nu}$ define the structure such that a general transformation near identity is given by:
   $$ \Lambda^{\mu}{}{\nu} \approx \delta^{\mu}{}{\nu} - i \sum{\mu\nu} \epsilon^{\mu\nu} G{\mu\nu} + O(\epsilon^2) $$
   where $\epsilon^{\mu\nu}$ represents the infinitesimal parameters. The ide…