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Abstract
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We investigate the infinite volume limit of the variational description of Euclidean
quantum fields introduced in a previous work. Focusing on two-dimensional theories for
simplicity, we prove in detail how to use the variational approach to obtain tightness of
without
cutoffs and a corresponding large deviation principle for any infinite volume limit. Any
infinite volume measure is described via a forward–backwards stochastic differential
equation in weak form (wFBSDE). Similar considerations apply to more general
theories. We
consider also the
model for
(the
so called full
regime) and prove uniqueness of the infinite volume limit and a variational characterization
of the unique infinite volume measure. The corresponding characterization for
theories is lacking due to the difficulty of studying the stability of the wFBSDE
against local perturbations.
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Keywords
constructive Euclidean quantum field theory, Boué–Dupuis
formula, stochastic analysis
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Mathematical Subject Classification
Primary: 60F10, 81T08
Secondary: 93E20
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Milestones
Received: 10 December 2021
Revised: 21 November 2022
Accepted: 3 March 2023
Published: 29 November 2023
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Publishers). |
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