Quantum Electrodynamics (Book): Difference between revisions

In a previous edition of volume 4, the theory of strong and weak nuclear forces was covered, as is mentioned in the preface to the second edition. In hindsight, it wasn't possible to predict the path of these developments which continue today; This shouldn't reflect negatively on this QED volume since the basics methods of the electromagnetic field have not changed, and continuing to experimental applications such as quantum optics will not feel anything lost in this treatment. The present authors and likely Landau himself had the foresight to restrict focus on what could be completely understood, and explain:

So what has gone beyond QED? The same finite-volume and finite-energy cutoffs made by Landau in the introduction are embedded into the mathematics of renormalization and effective field theory. As can be seen in Atiyah's book on gauge fields and Michelsohn-Lawson on Spin geometry, there is more geometric depth to the classical theory of fields. Standard QFT techniques dictate that we start with classical fields (either functions or gauge fields on bundles) and quantize them to produce a space of operators with desired commutation relations that also respect representation-theoretic aspects of the classical fields. At the quantum level, we measure amplitudes which are given by Green's functions/Correlation functions/propagators that relate the probabilities of processes relating individual points in space-time. These are integrated together to give individual operators on the abstract Hilbert space, which is captured in the Wightman formalism in the Fields and Strings book. Since then, multiple types of axiomatic QFT have emerged to pin down the space of QFTs as a mathematical and geometrical entity: