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I am studying about QFT and I'm trying to work with a time ordered product of three fields. In particular I have, \begin{equation} T\{\phi(x)\Psi(y)\bar{\Psi}(z)\} \end{equation} Where $T$ is the time ordered product. I'm writting this as follows \begin{equation} T\{\phi(x)\Psi(y)\bar{\Psi}(z)\}=\theta(x_0-y_0)\theta(y_0-z_0)\phi(x)\Psi(y)\bar{\Psi}(z)-\theta(x_0-z_0)\theta(z_0-y_0)\phi(x)\bar\Psi(z){\Psi}(y)+... \end{equation} Where the minus sign is due by the exchange of two fermionic fields and $\theta$ is the Heaviside step function. But is this expression correct? I don't know how to work with time ordered product with three operators so I supposed that we will have two step functions in each term but I'm not sure about it.

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The two terms you wrote are correct. Assuming the "$+...$" you wrote means "no minus sign whenever $\Psi(y)$ precedes $\bar\Psi(z)$ and include a minus sign whenever $\bar\Psi(z)$ precedes $\Psi(y)$", then your expression is right.

One way to justify this is Lorentz invariance. If $y$ and $z$ are space-like separated, there is no Lorentz invariant way to order them. In a frame where $y^0=z^0$, the equal time anti-commutation relations require that there is a minus sign if you switch the order of $\Psi(y)$ and $\bar{\Psi}(z)$. For Lorentz invariance, you need this minus sign to appear in any boosted frame.

Reference

David Tong's QFT lecture notes, Section 5.5 https://www.damtp.cam.ac.uk/user/tong/qft.html

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