Elliptic stochastic quantization of Sinh-Gordon QFT
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866912433763778560 |
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| author | Barashkov, Nikolay De Vecchi, Francesco C. |
| author_facet | Barashkov, Nikolay De Vecchi, Francesco C. |
| contents | The (elliptic) stochastic quantization equation for the (massive) $\cosh(βφ)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $β^2 < 4 π$), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov spaces in the continuum to analogous results for Besov spaces on the lattice. As a final result we show how to use the stochastic quantization equation to verify the Osterwalder-Schrader axioms for the $\cosh (βφ)_2$ quantum field theory, including the exponential decay of correlation functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2108_12664 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Elliptic stochastic quantization of Sinh-Gordon QFT Barashkov, Nikolay De Vecchi, Francesco C. Probability Mathematical Physics Analysis of PDEs 60H17, 81T08, 81T40 The (elliptic) stochastic quantization equation for the (massive) $\cosh(βφ)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $β^2 < 4 π$), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov spaces in the continuum to analogous results for Besov spaces on the lattice. As a final result we show how to use the stochastic quantization equation to verify the Osterwalder-Schrader axioms for the $\cosh (βφ)_2$ quantum field theory, including the exponential decay of correlation functions. |
| title | Elliptic stochastic quantization of Sinh-Gordon QFT |
| topic | Probability Mathematical Physics Analysis of PDEs 60H17, 81T08, 81T40 |
| url | https://arxiv.org/abs/2108.12664 |