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Quantum Field Theory: Interactions
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If you look at general relativity and quantum field theory (QFT), both represent fields using calculus: they both use differential equations describing continuous variables to represent fields which should strictly be sigma sums for the action in discrete interactions. This is why differential QFT leads to perturbative expansions with an infinite number of terms, each term corresponding to a Feynman diagram:
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The field-theoretic interests of the group find a natural complement not only in bound-state quantum electrodynamics, but ... in the study of critical phenomena using nonperturbative renormalization-group equations. E.g., the Wegner-Houghton equation has recently been used in order to infer the critical behaviour of layered sine-Gordon models, which have a range of potential applications, including solid-state physics (see [9] and references therein). In the coupled models, two-dimensional layers, each of which may undergo a Kosterlitz-Thouless type quantum phase transition, are coupled via a nonlinear interaction term. The transition temperature is modified as a function of the number of layers, and this surprising result may provide explanations for a number of phenomena.
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This workshop investigates the interactions between Representation Theories, Knot Theory, Topology, quantum Field Theory, Category Theory, and Mathematical Physics. This conference will be of great benefit to the researchers, recent Ph.Ds, and graduate students.
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For this reason perturbation theory makes up a large part of most publications on QFT. The importance of perturbative methods is understandable realizing that they establish the immediate contact between theory and experiment. Although the techniques of perturbation theory have become ever more sophisticated it is somewhat disturbing that perturbative methods could not be avoided even in principle. One reason for this unease is that perturbation theory is felt to be rather a matter of (highly sophisticated) craftsmanship than of understanding nature. Accordingly, the corpus of perturbative methods plays a small role in the philosophical investigations of QFT. What does matter... is in which sense the consideration of interaction effects the general framework of QFT.
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Interactions