Stochastic quantization and Osterwalder-Schrader axioms for quantum field theory models
Abstract
This PhD thesis constructs the P(Φ)2 Euclidean quantum field theory on 𝒮'(ℝ2). We first construct the finite-volume measure of the P(Φ)2 model on 𝒟'(𝕊R), where 𝕊R is a two-dimensional sphere of radius R∈ℕ+. To this end, we rely on Nelson's hypercontractivity estimate. We then use parabolic stochastic quantization and the energy method to construct the infinite-volume measure on 𝒮'(ℝ2). This requires establishing the global-in-time existence of solutions to the corresponding stochastic partial differential equations with fixed cutoffs. The remainder of the thesis is devoted to verifying the Osterwalder-Schrader axioms: regularity, reflection positivity, and invariance under translations, rotations, and reflections. This combination of axioms, which is crucial for obtaining a non-trivial local relativistic quantum field theory on Minkowski spacetime, had not been established in earlier constructions based on stochastic quantization.
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BibTeX
@misc{jahandideh2026stochastic,
title = {{Stochastic quantization and Osterwalder-Schrader axioms for quantum field theory models}},
author = {Azam Jahandideh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34063},
eprint = {2610.34063},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34063},
}
RIS
TY - UNPB
TI - Stochastic quantization and Osterwalder-Schrader axioms for quantum field theory models
AU - Azam Jahandideh
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34063
UR - https://arxiv.org/abs/2610.34063
AB - This PhD thesis constructs the P(Φ)_2 Euclidean quantum field theory on 𝒮'(ℝ^2). We first construct the finite-volume measure of the P(Φ)_2 model on 𝒟'(𝕊_R), where 𝕊_R is a two-dimensional sphere of radius R∈ℕ_+. To this end, we rely on Nelson's hypercontractivity estimate. We then use parabolic stochastic quantization and the energy method to construct the infinite-volume measure on 𝒮'(ℝ^2). This requires establishing the global-in-time existence of solutions to the corresponding stochastic partial differential equations with fixed cutoffs. The remainder of the thesis is devoted to verifying the Osterwalder-Schrader axioms: regularity, reflection positivity, and invariance under translations, rotations, and reflections. This combination of axioms, which is crucial for obtaining a non-trivial local relativistic quantum field theory on Minkowski spacetime, had not been established in earlier constructions based on stochastic quantization.
ER -