A. Zee, Quantum Field Theory in a Nutshell · Problem IV.3.3

Field Theory Redux

Physics — QFT

Problem

Consider a massless fermion field ψ\psi coupled to a scalar field ϕ\phi by fϕψˉψf\phi\bar{\psi}\psi in (1+1)(1 + 1)-dimensional spacetime. Show that VF=12π(fϕ)2log⁡ϕ2M2V_F = \frac{1}{2\pi}(f\phi)^2 \log \frac{\phi^2}{M^2} after a suitable counterterm has been added. This result is important in condensed matter physics, as we will see in chapter V.5 on the Peierls instability.

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