# Tagged Questions

In phase-space classical Hamiltonian mechanics, the Poisson bracket is an antisymmetric binary operation acting like a derivative.

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### Connection between Poisson Brackets and Symplectic Form

Jose and Saletan say the matrix elements of the Poisson Brackets (PB) in the ${q,p}$ basis are the same as those of the inverse of the symplectic matrix $\Omega^{-1}$, whereas the matrix elements ...
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In Dirac's book Principles of quantum mechanics (4th ed., pgs 87-88), he seems to give a very elementary argument as to how the commutator $[X,P]$ reduces to the Poisson brackets ${x,p}$ in the limit $... 1answer 165 views ### Yang-Mills constraints and Poisson brackets Let's have constraints for Yang-Mills theory: $$\varphi_{a} = \partial_{i}\pi^{i}_{a} - f_{abc}\pi^{b}_{i}A^{c}_{i}.$$ I have read the statement that$$\tag 1 [\varphi_{a}(\mathbf x), \varphi_{b}(\... 1answer 374 views ### Why is$\{Q, P\} = 1$for a canonical transformation? Why is$\{Q, P\} = 1$for a canonical transformation? Given$P(p,q)$and$Q(p,q)$. 2answers 692 views ### Canonical equal time commutation relations in QED I understand that to quantize the classical electromagnetic field one needs to impose commutation relations and express the field in terms of creation and annihilation operators. I notice that the ... 2answers 112 views ### Find the error: If$L_x$and$L_y$are zero, then$L_z\$ is conserved

From Goldstein's Classical Mechanics (2nd ed.), problem 38 of chapter 9 basically says the following: It's been shown that the Poisson bracket of two constants of the motion is also a constant of ...