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I am trying to drive constraints of a Lagrangian density by Dirac Hamiltonian method. But I encountered a problem with calculating one type of Poisson Bracket:

{[itex]\varphi,\partial_x\pi[/itex]}=?

where [itex]\pi[/itex] is conjugate momentum of [itex]\varphi[/itex]. I do not know for this type Poisson Bracket I can use part-by-part integration or not. I mean

{[itex]\varphi,\varphi\partial_x\pi[/itex]}= -[itex]\varphi[/itex]

Cheeeers!

Vahid

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# Poisson Bracket - Constrained system

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