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Canonical transformations in the covariant phase space formalism

Ref. 1 is talking about the Peierls bracket in the Lagrangian formalism. It is equivalent to the presymplectic structure in the covariant Hamiltonian formalism, cf. e.g. section 4.1 in Ref. 3. Ref. 1 ...
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Commutation of the Hamiltonian with the generator of boost

...From the above, we see that $$\{M^{0i}, H\} = P^i$$ No, you should have: $$ \{M^{0i}, H\} = -P^i $$ ...Why is it that $\frac{d}{dt}M^{0i}\neq \{H, M^{0i}\}$? Can someone please explain? It's ...
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