Answer by Qmechanic for Is it valid to replace the equations of motion inside...
Yes, to show that an infinitesimal transformation $\delta$ is a symmetry of the equations of motion $\text{EOM}=0$, one may use the equations of motion $\text{EOM}=0$ (and consequences thereof) to...
View ArticleAnswer by Bob Bee for Is it valid to replace the equations of motion inside a...
Yes, in classical field theory and classical Lagrangian systems the Noether Theorem is valid on shell, i.e., taking the eom's into account. The equivalent quantum field theory version for expectation...
View ArticleAnswer by Valter Moretti for Is it valid to replace the equations of motion...
Yes it is valid. The problem can be viewed this way. There is a manifold, a fiber bundle (a jet bundle actually) $A$, with basis $\mathbb R$ where the coordinate $t$ ranges and fibers $Q_t$ locally...
View ArticleIs it valid to replace the equations of motion inside a symmetry?
For example, this symmetry:$$\delta q^{i}=\epsilon(q^{i}-2\dot{q}^{i}t)$$it's derivative is:$$\delta\dot{q}^{i}=-\epsilon(\dot{q}^i +2\ddot{q}^i t)$$There appears $\ddot{q}^{i}$ in this expression, so...
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