1) There are already many good answers explaining the conventional theory and observations. Nevertheless, related to comments by lurscher and  Adam Zalcman, it seems appropriate to mention the [Nambu bracket](http://en.wikipedia.org/wiki/Nambu_mechanics), which is a Poisson-like bracket 

$$ \{ f,g,h \} $$

with 3 function entries, originally invented by Nambu in 1973, purportedly in a failed attempt to explain $SU(3)$ symmetry in quarks. Already Nambu discusses an operator version

$$ [\hat{f},\hat{g},\hat{h} ], $$

and one can imagine some kind of uncertainty relation associated to this, where canonical variables come in triplets. Unfortunately, the subject so far has remained just theoretical speculations. [Authors even don't agree what should replace the [Jacobi identity](http://en.wikipedia.org/wiki/Jacobi_identity) for the Poisson bracket  $\{ f,g\}$, although most think it should be the so-called Filippov fundamental Identity (FI).]

2) Recently in 2008, the Nambu-bracket has been used in the [Bagger–Lambert–Gustavsson](http://en.wikipedia.org/wiki/Bagger%E2%80%93Lambert%E2%80%93Gustavsson_action) M2 brane proposal.

3) The exist various generalizations to higher Nambu brackets 

$$ \{ f_1,\ldots ,f_n \} $$

with $n$ entries. 

4) For more information, see this [review](http://arxiv.org/abs/1005.1028).