# Peierls bracket

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In theoretical physics, the **Peierls bracket** is an equivalent description of the Poisson bracket. It directly follows from the action and does not require the canonical coordinates and their canonical momenta to be defined in advance.

The bracket

is defined as

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

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