3. Poisson brackets Write down the Poisson brackets between the angular momentum L Fxp and an...
3. Poisson brackets Write down the Poisson brackets between the angular momentum L Fxp and an arbitrary vector field that depends on the position and momentum AF, p). Explain which calculation rules for the Poisson brackets can be used to calculate Poisson brackets between vector quanti ties Using this relation calculate the following Poisson brackets a) Li, r} b) {Li, Pj} e) Li, Lj} Hint: Use the expression Li (Fxp) = eijkrjPk for the components of the angular momentum. (Note that the Einstein's sum convention was used, i.e. indices appearing twice in a product are summed over. The explicit summation sign is omitted. You can use the the fundament al Poisson brackets from the lecture, or just work out the partial derivatives in a specific set of canonical variables. State the steps you are performing and which calculation rules you are using