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Quantum Theory: Quantum Field Theories
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Finding the proper axioms for quantum field theory is still an open and difficult problem in mathematics. One of the Millennium Prize Problems—proving the existence of a mass gap in Yang-Mills theory—is linked to this issue.
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John Baez has written this article to provide a "gut-level understanding" on the topic of renormalization in quantum field theory. It assumes knowledge of quantum physics which is, at least, advanced undergraduate level.
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The study of quantum field theory is alive and flourishing, as are applications of this method to many physical problems. It remains one of the most vital areas of theoretical physics today, providing a common language to many branches of physics.
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String theory is about having a quantum field theory whereby the entity being considered as fundamental is not a point within the field but a string instead. This leads to all kinds of great things like a prediction for number of dimensions, a prevention of UV divergences in scattering processes and best of all, a derivation of gravity within a quantum framework.
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Quantum Field Theories