Question

Use the mode expansion of the fermion field, given in eqn (9.7.19), and the anticommutation relations of the operators $A(\theta)$ and $A^{\dagger}(\theta)$, to compute the correlation functions $$ \begin{aligned} G_1(x, t) & =\langle 0|\Psi(x, t) \Psi(0,0)| 0\rangle \\ G_2(x, t) & =\langle 0|\bar{\Psi}(x, t) \Psi(0,0)| 0\rangle . \end{aligned} $$

   Use the mode expansion of the fermion field, given in eqn (9.7.19), and the anticommutation relations of the operators $A(\theta)$ and $A^{\dagger}(\theta)$, to compute the correlation functions
$$
\begin{aligned}
G_1(x, t) & =\langle 0|\Psi(x, t) \Psi(0,0)| 0\rangle \\
G_2(x, t) & =\langle 0|\bar{\Psi}(x, t) \Psi(0,0)| 0\rangle .
\end{aligned}
$$

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Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

Giuseppe Mussardo 1st Edition

Chapter 9, Problem 4

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Step 1

According to eqn (9.7.19), the mode expansion of the fermion field in (1+1) dimensions can be generally expressed as: $$ \Psi(x,t) = \int \frac{d\theta}{2\pi} \left[ e^{-i(m\sinh\theta t - mx\cosh\theta)} A(\theta) + e^{i(m\sinh\theta t - mx\cosh\theta)} Show more…

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Use the mode expansion of the fermion field, given in eqn (9.7.19), and the anticommutation relations of the operators $A(\theta)$ and $A^{\dagger}(\theta)$, to compute the correlation functions $$ \begin{aligned} G_1(x, t) & =\langle 0|\Psi(x, t) \Psi(0,0)| 0\rangle \\ G_2(x, t) & =\langle 0|\bar{\Psi}(x, t) \Psi(0,0)| 0\rangle . \end{aligned} $$

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