Consider a harmonic oscillator, with Lagrangian (L=left(dot{q}^{2}-omega^{2} q^{2} ight) / 2). Using a naive generalization of the

Consider a harmonic oscillator, with Lagrangian \(L=\left(\dot{q}^{2}-\omega^{2} q^{2}\right) / 2\). Using a naive generalization of the Gaussian integration, show that the generating functional is of the type given in exercise 5. Write a formal expression for \(\Delta\left(t, t^{\prime}\right)\).