A representation of quantum field Hamiltonian in a $p$-adic Hilbert space
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 3, pp. 355-374
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Gaussian measures on infinite-dimensional $p$-adic spaces are introduced and the corresponding $L_2$-spaces of $p$-adic valued square integrable functions are constructed. Representations of the infinite-dimensional Weyl group are realized in $p$-adic $L_2$-spaces. There is a formal analogy with the usual Segal representation. But there is also a large topological difference: parameters of the $p$-adic infinite-dimensional Weyl group are defined only on some balls (these balls are additive subgroups). $p$-Adic Hilbert space representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constructed. Many Hamiltonians with potentials which are too singular to exist as functions over reals are realized as bounded symmetric operators in $L_2$-spaces with respect to a $p$-adic Gaussian measure.
@article{TMF_1997_112_3_a0,
author = {S. A. Albeverio and A. Yu. Khrennikov and R. Cianci},
title = {A representation of quantum field {Hamiltonian} in a $p$-adic {Hilbert} space},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {355--374},
publisher = {mathdoc},
volume = {112},
number = {3},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_3_a0/}
}
TY - JOUR AU - S. A. Albeverio AU - A. Yu. Khrennikov AU - R. Cianci TI - A representation of quantum field Hamiltonian in a $p$-adic Hilbert space JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1997 SP - 355 EP - 374 VL - 112 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1997_112_3_a0/ LA - ru ID - TMF_1997_112_3_a0 ER -
%0 Journal Article %A S. A. Albeverio %A A. Yu. Khrennikov %A R. Cianci %T A representation of quantum field Hamiltonian in a $p$-adic Hilbert space %J Teoretičeskaâ i matematičeskaâ fizika %D 1997 %P 355-374 %V 112 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1997_112_3_a0/ %G ru %F TMF_1997_112_3_a0
S. A. Albeverio; A. Yu. Khrennikov; R. Cianci. A representation of quantum field Hamiltonian in a $p$-adic Hilbert space. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 3, pp. 355-374. http://geodesic.mathdoc.fr/item/TMF_1997_112_3_a0/