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تسجيل مستخدم جديدStochastic quantization associated with the $exp(Phi)_2$-quantum field model driven by space-time white noise on the torus
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We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the $exp (Phi)_{2}$-quantum field model or H{o}egh-Krohns model. In the present paper, we study the stochastic quantization of this model by singular stochastic partial differential equations, which is recently developed. By the method, we construct a unique time-global solution and the invariant probability measure of the corresponding stochastic quantization equation, and identify with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.
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The present paper is a continuation of our previous work on the stochastic quantization of the $exp(Phi)_2$-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for si
ngular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full $L^{1}$-regime $vertalphavert<sqrt{8pi}$ of the charge parameter $alpha$. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.
(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) We study the construction of the $Phi^3_3$-measure and complete the program on the (non-)construc
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A new construction of non-Gaussian, rotation-invariant and reflection positive probability measures $mu$ associated with the $varphi ^4_3$-model of quantum field theory is presented. Our construction uses a combination of semigroup methods, and metho
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