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p-adic field theories

Investigate quantum field theory on p-adic spaces and its relation to QFT on continuous spacetime — nonlocal, hierarchical constructions with powerful properties such as a non-renormalization theorem.

Investigate quantum field theory on p-adic spaces and its relation to QFT on continuous spacetime inspired from number theory. The simplest constructions of QFT on p-adic spaces are nonlocal, have an inherently hierarchical nature, and enjoy various powerful properties such as a non-renormalization theorem, while sharing deep connections with their continuous counterparts.