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Rigorous quantum field theory functional integrals over the p-adics

Mathematical Physics & Probability

Speaker: Abdelmalek Abdesselam, University of Virginia
Location: 1147 MSB
Start time: Wed, May 16 2012, 4:10PM

I will present the results of joint work with Ajay Chandra and Gianluca Guadagni regarding the construction of probability measures on the space of distributions over a three-dimensional p-adic space-time. The particular model we consider is scale-invariant and governed by a nontrivial renormalization group fixed point. The latter is an analogue of the Wilson-Fisher fixed point related to the three-dimensional Ising model. The main new ingredient of our results is an extension of the renormalization group methods by Brydges and collaborators to the case of nonuniform potentials. This allows us to construct the correlation functions of the elementary field as well as the composite squared field.