Editing Quantum Electrodynamics (Book)
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* radiation and application of the scattering/S-matrix concepts introduced in volume 3 | * radiation and application of the scattering/S-matrix concepts introduced in volume 3 | ||
* perturbation and Feynman graph techniques to compute particle-particle interactions | * perturbation and Feynman graph techniques to compute particle-particle interactions | ||
And the level of mathematics developed is sufficient to continue to apply it to the quantum theory of metals and superfluid helium as in | And the level of mathematics developed is sufficient to continue to apply it to the quantum theory of metals and superfluid helium as in volume 9, condensed matter physics. | ||
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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. The representation theory arguments in Woit's and Mackey's books are used by Weinberg to pin down particle species and interactions, determining much of the basic structure of the relativistic theory from first principles alone. This is the single biggest practical step in how the theory is viewed by physicists since its inception by Jordan, Born, and Heisenberg. 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, or equivalently directly compute the expectation values of these operators with path integrals using the classical field Lagrangian. Classical gauge theory has been used to further describe dynamical properties of the quantum theory, famously such as Weinberg and Salam's Electroweak theory and Anderson-Higgs' symmetry breaking. At the quantum level, we measure complex 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: | 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. The representation theory arguments in Woit's and Mackey's books are used by Weinberg to pin down particle species and interactions, determining much of the basic structure of the relativistic theory from first principles alone. This is the single biggest practical step in how the theory is viewed by physicists since its inception by Jordan, Born, and Heisenberg. 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, or equivalently directly compute the expectation values of these operators with path integrals using the classical field Lagrangian. Classical gauge theory has been used to further describe dynamical properties of the quantum theory, famously such as Weinberg and Salam's Electroweak theory and Anderson-Higgs' symmetry breaking. At the quantum level, we measure complex 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: | ||