Abstract
It is shown that some Gaussian and non-Gaussian scaling invariant p-adic field theories are invariant under the group of transformations which conserve the p-adic norm of the cross-ratio of any four points. This group can be treated as a p-adic conformal group. It has a continuation on the Bruhat—Tits tree, being an automorphism group of that tree. The models also have tree continuation, in particular the binary correlation function of the tree model is a spherical function.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
VolovichI. V., Classical Quantum Gravity 4, 183 (1987).
FreundP. G. and OlsonM., Phys. Lett. 199B, 186 (1987).
GrossmanB., Phys. Lett. 197B, 101 (1987).
FreundP. G. and WittenE., Phys. Lett. 199B, 191 (1987).
FramptonP. and OkadaY., Phys. Rev. Lett. 60, 484 (1988).
ParisiG., Mod. Phys. Lett. A3, 639 (1988).
GervaisJ. L., Phys. Lett. 201B, 306 (1988).
LernerE. Yu. and MissarovM. D., Teoret. Mat. Fiz. 78, 248 (1989) (in Russian).
LernerE. Yu. and MissarovM. D., Comm. Math. Phys. 121, 35 (1989).
Missarov, M. D., Advances in Soviet Mathematics, v. 3, to be published.
MelzerE., Internat. J. Modern Phys. A4, 4877 (1989).
ZabrodinA. V., Comm. Math. Phys. 123, 465 (1989).
ChehovL. O. and ZinovievA. V., Comm. Math. Phys. 130, 623 (1990).
BleherP. M. and MissarovM. D., Comm. Math. Phys. 74, 255 (1980).
ManinYu. I., in Sovrem. Probl. Mat. 3, 5. Moscow, VINITI, 1974 (in Russian).
CartierP., in Harmonic Homogeneous Spaces, Proc. Sympos. Math. Vol. 26, Amer. Math. Soc. Providence, R.I., 1973, p. 419.
BleherP. M. and SinaiY. G., Comm. Math. Phys. 45, 247 (1975).
Collet, P. and Eckmann, J. P., Lecture Notes in Phys. 74 (1978).