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\(p\)-adic conformal invariance and the Bruhat-Tits tree. (English) Zbl 0746.22018
The symmetry properties of \(p\)-adic scaling invariant field theories are investigated. It is shown that some Gaussian and non-Gaussian scaling invariant \(p\)-adic field theories are invariant under the group which conserves the \(p\)-adic norm of the cross-ratio of any four points. This group has a continuation on the Bruhat-Tits tree as an automorphism group of this tree.

MSC:
22E70 Applications of Lie groups to the sciences; explicit representations
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
43A80 Analysis on other specific Lie groups
22E35 Analysis on \(p\)-adic Lie groups
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