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1. Infinitesimal Parameter

   Linked via "conserved quantity"

   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/), often denoted $\alpha$, which dictates the am…

2. Lagrangian Density

   Linked via "conserved quantities"

   Relationship to Conservation Laws (Noether's Theorem)
   A deep connection exists between continuous symmetries of the Lagrangian density and conserved quantities, formalized by Noether's theorem. If the Lagrangian density transforms covariantly under a continuous transformation parameterized by a variable $\theta$, such that the resulting change in $\mathcal{L}$ is compensated exactly by the divergence of a four-vector $J^\mu$, then a conserved current $J^\mu$ exists.
   Specifica…

3. Lorentz Group

   Linked via "conserved quantities"

   where $\theta_{\nu}^{\mu}$ are infinitesimal parameters which must satisfy the symmetry condition, yielding:
   $$ \theta^{\eta\nu} = -\theta^{\nu\eta} $$
   The conserved quantities arising from the invariance of the Lagrangian Density under these transformations are the angular momentum tensor and the boost generator tensor (often called the kinetic momentum tensor, $Q^i$, in older literature) [2].
   The Spinor Representation and Particle Classification