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The question starts with why Poisson brackets (in constrained systems) gives different relation if we substitute the constraints before or after expanding the bracket, and why this difference in rela …

Let me start by asking why we need a Poisson bracket like structure on the Hamiltonian phase space? Say we have a constraint, why do we go through the trouble of defining a Dirac bracket structure on …

What happens to the poisson bracket structure of Hamiltonian phase space if We have some constraints in $p$ and $q$. What physical aspects this structure represents?

Why exactly do we need $$ \{q^i,p_j\}=\delta^i_j,$$ where $\delta^i_j$ is Kronecker delta and $\{\cdot,\cdot\}$ is the Poisson bracket? What happens to the phase space structure if these fundamental …

The question starts with why Poisson brackets (in constrained systems) gives different relation if we substitute the constraints before or after expanding the bracket, and why this difference in relat …