1. The projection postulate as commonly used nowadays is due to G. Lüders, Ann. Phys. 8, 323 (1951). For observables with degenerate eigenvalues his formulation differs from that of J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer (Berlin 1932) (English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955), Chapter V.1. The projection postulate intends to describe the effects of an ideal measurement on the state of a system, and it has been widely regarded as a useful tool.
2. For a simplified case one can see this directly as follows. The $$\omega^{2}$$ inherent in $$d^{3} k$$ and the $$\omega_{k}$$ in $$\kappa $$ give a factor of $$\omega^{3}$$ . If this $$\omega^{3}$$ is omitted in the definition of $$\kappa $$ then the result can be seen by a straightforward calculation of the double integral in (6.22). The general case can be reduced to this by partial integration. We note that for $$\omega_{0}$$ in the microwave range the condition $$t^{\prime}\, - \,t_i \gg \,\omega _0^{ - 1}$$ does not hold. However, the radiative coupling of such levels is extremely small and is usually neglected in applications.
3. D. Alonso, I. de Vega, Phys. Rev. Lett. 94, 200403 (2005)
4. A. Beige, Doctoral Dissertation, Universität Göttingen, Germany (1997)
5. A. Beige, G.C. Hegerfeldt, Phys. Rev. A 53, 53 (1996)