TY  - JOUR
AB  - We prove the existence of global solutions to singular SPDEs on Rd with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions d=4, 5 and in the parabolic setting for d = 2, 3. We prove uniqueness and coming down from infinity for the parabolic equations. A motivation for considering these equations is the construction of scalar interacting Euclidean quantum field theories. The parabolic equations are related to the phi d4 Euclidean quantum field theory via Parisi-Wu stochastic quantization, while the elliptic equations are linked to the phi d-24 Euclidean quantum field theory via the Parisi-Sourlas dimensional reduction mechanism.
DA  - 2019
DO  - 10.1007/s00220-019-03398-4
LA  - eng
IS  - 3
M2  - 1201
PY  - 2019
SN  - 0010-3616
SP  - 1201-1266
T2  - Communications in Mathematical Physics
TI  - Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29360161
Y2  - 2024-11-22T06:49:22
ER  -