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What does Qmechanic mean by “equality modulo equations of motion” when talking about Lagrangian formulation/formalism and so on?

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    $\begingroup$ You should probably edit your post in order to add more detail and context. $\endgroup$
    – RedGiant
    Jan 6, 2021 at 22:14

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I guess I should answer this :)

In the context of the Lagrangian formalism the equations of motion (EOM) refer to Euler-Lagrange (EL) equations.

The phrase "equality modulo EOM" means that a left-hand side is equal to a right-hand side of an equation if one uses the EOM.

It is often important to keep track of when one uses EOM. Sometimes one is not allowed to assume the EOM. A common error is a premature use of EOM in the stationary action principle. For an example of what can go wrong, see this or this Phys.SE posts.

See also this related Phys.SE post.

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