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| (1) |
Set theta as an anticommutative prefix (see Setup)
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| (2) |
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
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| (5) |
A taylor expansion as well as an exact expansion for it respectively performed with Gtaylor and ToFieldComponents
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| (8) |
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 coefficient of order 1
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| (11) |
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| (13) |
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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