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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.

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
Full Text: DOI
[1] VolovichI. V., Classical Quantum Gravity 4, 183 (1987).
[2] FreundP. G. and OlsonM., Phys. Lett. 199B, 186 (1987).
[3] GrossmanB., Phys. Lett. 197B, 101 (1987).
[4] FreundP. G. and WittenE., Phys. Lett. 199B, 191 (1987).
[5] FramptonP. and OkadaY., Phys. Rev. Lett. 60, 484 (1988).
[6] ParisiG., Mod. Phys. Lett. A3, 639 (1988).
[7] GervaisJ. L., Phys. Lett. 201B, 306 (1988).
[8] LernerE. Yu. and MissarovM. D., Teoret. Mat. Fiz. 78, 248 (1989) (in Russian).
[9] LernerE. Yu. and MissarovM. D., Comm. Math. Phys. 121, 35 (1989). · Zbl 0671.22011
[10] Missarov, M. D., Advances in Soviet Mathematics, v. 3, to be published. · Zbl 1284.82029
[11] MelzerE., Internat. J. Modern Phys. A4, 4877 (1989).
[12] ZabrodinA. V., Comm. Math. Phys. 123, 465 (1989). · Zbl 0676.22006
[13] ChehovL. O. and ZinovievA. V., Comm. Math. Phys. 130, 623 (1990). · Zbl 0703.22010
[14] BleherP. M. and MissarovM. D., Comm. Math. Phys. 74, 255 (1980).
[15] ManinYu. I., in Sovrem. Probl. Mat. 3, 5. Moscow, VINITI, 1974 (in Russian).
[16] CartierP., in Harmonic Homogeneous Spaces, Proc. Sympos. Math. Vol. 26, Amer. Math. Soc. Providence, R.I., 1973, p. 419.
[17] BleherP. M. and SinaiY. G., Comm. Math. Phys. 45, 247 (1975).
[18] Collet, P. and Eckmann, J. P., Lecture Notes in Phys. 74 (1978).
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