# Instructional examples of QFT

Where can one find some concrete physical problems (with solutions) that illustrates the uselfullness and power of QFT? These must not be solvable by QM or SR alone.

It would be good if the problem utilizes the most central QFT concepts. I am trying to learn QFT but it looks like only some mathematical definitions.

Concrete QFT calculations which shows agreement with physical experiment to high accuracy.

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For an approach to scattering in a non-equilibrium environment, have a look at Quantum Kinetics in Transport and Optics of Semiconductors by Hartmut J. W. Haug & Antti-Pekka Jauho. The idea is mostly that you cannot really use standard QM if the number of particles in your system is not constant. – Claudius Dec 11 '12 at 9:52
Lamb shift calculation might be a good starting point. – twistor59 Dec 11 '12 at 10:24
Right, twistor, that's a precision calculation in QFT, much like the most precise prediction in science, the anomalous moment of the electron. But even some tree-level processes such as positron-electron annihilation do totally need QFT. – Luboš Motl Dec 11 '12 at 10:41
This is exactly what the first chapter of Peskin and Schroder attempts to do, by outlining the calculation of the cross-section for $e^{+} + e^{-} \rightarrow \mu^{+} + \mu^{-}$ – Jerry Schirmer Dec 12 '12 at 17:24