Schwinger-Dyson equations derivation

[simonjech]

This is the part of Schwinger-Dyson equations derivation. I did not understand how can we obtain the commutator in the last line of the picture. I understand why the delta functions appeared from Heaviside functions but there is no minus sign in any term so how can we get the commutator? Anticommutator would make more sence for me.

 

[julian]

Write down $\theta (-t)$ in terms of $\theta (t)$. Drawing the graph of $\theta (-t)$ helps.

 

[malawi_glenn]

Or just use the chain rule for differentiation

 

[simonjech]

I think that i figured it out. The problem was that I did not realized that

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