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In theoretical physics, the Peierls bracket is an equivalent description^{[ clarification needed]} 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.^{[ clarification needed]}

The bracket^{[ clarification needed]}

${\displaystyle [A,B]}$

is defined as

${\displaystyle D_{A}(B)-D_{B}(A)}$,

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.

References

This article incorporates material from the Citizendium article " Peierls bracket", which is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License but not under the GFDL.

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

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