AntiCommutator

Description

AntiCommutator[x, y] = c defines the anti-commutator of the non commuting objects x and y.

See also:  Commutator, CommutatorExplicit, DeclareNonCommutative, DotSimplify.

Examples

This declares a and b as noncommutative variables.

DeclareNonCommutative[a, b]

AntiCommutator[a, b]

CommutatorExplicit[%]

CommutatorExplicit[
      AntiCommutator[a + b, a - 2  b ]]

DotSimplify[AntiCommutator[a + b, a - 2  b ]]

\(DeclareNonCommutative[c, d, \(c\&~\), \(d\&~\)]\)

Defining {c,d} = z results in replacements of c.d by z-d.c.

AntiCommutator[c, d]  =  z

DotSimplify[ d  .  c  .  d ]

\(AntiCommutator[\(d\&~\), \(c\&~\)]\  = \ \(z\&~\)\)

\(DotSimplify[\ \(d\&~\)\  . \ \(c\&~\)\  . \ \(d\&~\)\ ]\)

\(UnDeclareNonCommutative[a, b, c, d, \(c\&~\), \(d\&~\)]\)

Unset[AntiCommutator[c, d]]

\(Unset[AntiCommutator[\(d\&~\), \(c\&~\)]]\)