Einj
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Hi all! I'm sorry if this question has been already asked in another post...
I'm studying the path integrals formalism in QED. I'm dealing with the functional generator for fermionic fields. My question is:
The generating functional is:
$$Z_0=e^{-i\int{d^4xd^4y \bar{J}(x)S(x-y)J(y)}}$$
Where $$J(x)$$ and $$\bar{J}(x)$$ are Grassmann numbers.
When I have to extract Green function from the generating functional I have to perform, for example, a functional derivative rispect to J(z). Does the functional derivative follow the same rule as the ordinary derivative? Do I have to anticommutate $$\bar{J}$$ and $$J$$ before deriving??
Thaks to all
Einj
I'm studying the path integrals formalism in QED. I'm dealing with the functional generator for fermionic fields. My question is:
The generating functional is:
$$Z_0=e^{-i\int{d^4xd^4y \bar{J}(x)S(x-y)J(y)}}$$
Where $$J(x)$$ and $$\bar{J}(x)$$ are Grassmann numbers.
When I have to extract Green function from the generating functional I have to perform, for example, a functional derivative rispect to J(z). Does the functional derivative follow the same rule as the ordinary derivative? Do I have to anticommutate $$\bar{J}$$ and $$J$$ before deriving??
Thaks to all
Einj