Why is there this extra term for this correlation function?

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The discussion focuses on the computation of the correlation function involving a Dirac field ##\Psi## and a scalar field ##\varphi##, specifically $$<0|T \Psi _\alpha (x) \Psi _\beta (y) \varphi (z_1) \varphi (z_2)|0>$$. The inclusion of the term with ##z_1## and ##z_2## exchanged is crucial for ensuring the symmetry properties of the correlation function, which is essential in quantum field theory. The correlation function is expressed through functional derivatives and involves the propagators ##S(x-w_1)## and ##\Delta(z_i - w_i)##, emphasizing the importance of these terms in maintaining consistency in calculations.

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Let's say we have a Dirac field ##\Psi## and a scalar field ##\varphi## and we want to compute this correlation function $$<0|T \Psi _\alpha (x) \Psi _\beta (y) \varphi (z_1) \varphi (z_2)|0>$$ $$= \frac {1}{i} \frac{\delta}{\delta \overline{\eta}_\alpha(x)} i \frac{\delta}{\delta \eta_\beta(y)} \frac {1}{i} \frac{\delta}{\delta J(z_1)} \frac {1}{i} \frac{\delta}{\delta J(z_2)} iW(\overline{\eta}, \eta, J) |_{\overline{\eta}, \eta, J = 0}$$ $$= c \int d^4 w_1 d^4 w_2 [S(x-w_1)S(w_1 - w_2) S(w_2 -y)]_{\alpha \beta} \Delta (z_1 - w_1) \Delta (z_2 - w_2) + \mathrm{the\ previous\ term\ with \ z_1\ and\ z_2\ exchanged}$$
where c is a constant

My question is: why do we have the last term in the equation? Why do we include the term with ##z_1## and ##z_2## exchanged?
 
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