A. Zee, Quantum Field Theory in a Nutshell · Problem VII.4.7

Field Theory Redux

Physics — QFT

Problem

For

V(\phi) = \frac{1}{2}m^2\phi^2 + g\phi^4

, determine

\rho(E)

. For

m^2

sufficiently negative (the double well potential again) we expect the density of eigenvalues to split into two pieces. This is evident from the Dyson gas picture. Find the critical value

m_c^2

. For

m^2 < m_c^2

the assumption of

G(z)

having only one cut used in the text fails. Show how to calculate

\rho(E)

in this regime.

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