GrassmannParity(expression)

Set theta as an anticommutative prefix (see Setup)

The parity of (3) is 0 despite the presence of anticommutative variables: a product of two of them is overall commutative

A commutative function of commutative and anticommutative variables: its parity is zero

A taylor expansion as well as an exact expansion for it respectively performed with Gtaylor and ToFieldComponents

Note that the expansion performed with Gtaylor does not preserve the parity of (5) while the one performed with ToFieldComponents does:

The coefficient of order zero of both expansions preserves the parity; the difference appears with respect to the the coefficient of order 1

To understand this difference between the Taylor and the exact expansions performed with Gtaylor and ToFieldComponents see the expansion's definitions in the respective help pages

anticommutative, Coefficients, commutative, Physics, Physics conventions, Physics examples, relation, series, Setup, ToFieldComponents