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I already asked this in the physics forum but without much attention, so I thought it might attract more attention here. Is there an integral expression for the Poisson bracket that can be derived ...

Let $T$ be a linear algebraic torus over $\mathbb C$ and $X$ be a smooth quasi-projective symplectic $T$-variety. Also, assume that the action of $T $ is free and $X/T$ exists as a smooth variety. Is ...