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1. Infinitesimal Parameter

   Linked via "physical law"

   Physical Manifestations and Dimensionality
   The physical interpretation of an Infinitesimal Parameter is heavily dependent on the specific physical law or transformation it governs. In canonical mechanics, parameters related to time evolution are often designated $\delta t$, where the subscript denotes an instantaneous interval. Conversely, in field theory, the parameter is usually dimensionless or carries the inverse dimension of an action/…

2. Lorentz Group

   Linked via "physical law"

   The Lorentz group $O(1, 3)$ forms the homogeneous part of the Poincaré group $\text{ISO}(1, 3)$. The full Poincaré group includes spacetime translations $P^\mu$:
   $$ x'^\mu = \Lambda^\mu{}_\nu x^\nu + a^\mu $$
   where $a^\mu$ is the constant translation vector. The commutation relations of the generators $P^\mu$ and $J^{\mu\nu}$ (the full set of ten generators) define the structure of this larger group, which governs all symmetries of [Minkowski spacetime](/entries/minkow…