Peierls bracket

{{short description|Theoretical physics}}

{{More citations needed|date=July 2007}}

In theoretical physics, the Peierls bracket is an equivalent description{{clarify|reason=Sorry, but does this mean it is the same as the Poisson bracket?|date=August 2016}} of the Poisson bracket. It can be defined directly from the action and does not require the canonical coordinates and their canonical momenta to be defined in advance.{{clarify|reason=Does the Peierls bracket even require the action? The Poisson bracket does not need the action to be defined. Nor does it need a choice of canonical coordinates. It only needs the symplectic structure.|date=August 2016}}

The bracket{{clarify|reason=Now this looks like the Lie bracket. Is the Peierls bracket the Lie Bracket?|date=August 2016}}

:$[A,B]$

is defined as

:$D\_A(B)-D\_B(A)$,

as the difference between some kind of action of one quantity on the other, minus the flipped term.

In quantum mechanics, the Peierls bracket becomes a commutator i.e. a Lie bracket.