Editing 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 (physics)|action]] and does not require the [[canonical coordinate]]s 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}}

:<math>[A,B]</math>

is defined as

:<math>D_A(B)-D_B(A)</math>,

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 of vector fields|Lie bracket]].

==References==
{{Citizendium}}
<references />

Peierls, R. "The Commutation Laws of Relativistic Field Theory,"
Proc. R. Soc. Lond. August 21, 1952 214 1117 143-157.

[[Category:Theoretical physics]]


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