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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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