Monte Carlo Evaluation of the Continuum Limit of the Two-Point Function of the Euclidean Free Real Scalar Field Subject to Affine Quantization
We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point function near the continuum limit at finite volume. Our investigation shows that affine quantization is ab...
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| Published in | Journal of statistical physics Vol. 184; no. 3 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.09.2021
Springer Springer Nature B.V |
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| Abstract | We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point function near the continuum limit at finite volume. Our investigation shows that affine quantization is able to give meaningful results for the two-point function for which is not available an exact analytic result and therefore numerical methods are necessary. |
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| AbstractList | We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point function near the continuum limit at finite volume. Our investigation shows that affine quantization is able to give meaningful results for the two-point function for which is not available an exact analytic result and therefore numerical methods are necessary. |
| ArticleNumber | 28 |
| Audience | Academic |
| Author | Fantoni, Riccardo Klauder, John R. |
| Author_xml | – sequence: 1 givenname: Riccardo orcidid: 0000-0002-5950-8648 surname: Fantoni fullname: Fantoni, Riccardo email: riccardo.fantoni@posta.istruzione.it organization: Dipartimento di Fisica, Università di Trieste – sequence: 2 givenname: John R. surname: Klauder fullname: Klauder, John R. organization: Department of Physics and Department of Mathematics, University of Florida |
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| Keywords | Monte Carlo method 05.10.Ln Euclidean free real scalar field-theory 03.50.-z Continuum limit 02.70.Ss 02.70.Uu Two-point function Affine quantization 11.10.Gh 11.10.Kk Canonical quantization 11.10.-z |
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| References | KalosMHWhitlockPAMonte Carlo Methods2008HobokenWiley10.1002/9783527626212 Fantoni, R.: Monte Carlo evaluation of the continuum limit of (ϕ12)3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi ^{12})_3$$\end{document}, J. Stat. Mech. 083102 (2021) MetropolisNRosenbluthAWRosenbluthMNTellerAMTellerEEquation of state calculations by fast computing machinesJ. Chem. Phys.19531087211431.65006 KlauderJRAn ultralocal classical and quantum gravity theoryJ. High Energy Phys. Gravit. Cosmol.2020665610.4236/jhepgc.2020.64044 Klauder, J.R.: The benefits of affine quantization. J. High Energy Phys. Gravit. Cosmol. 6, 175 (2020) FantoniRKlauderJRAffine Quantization of (φ4)4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varphi ^{4})_4$$\end{document} Succeeds While Canonical Quantization FailsPhys. Rev. D20211030760132021PhRvD.103g6013F425993810.1103/PhysRevD.103.076013 CeperleyDMPath integrals in the theory of condensed heliumRev. Mod. Phys.1995672791995RvMP...67..279C10.1103/RevModPhys.67.279 DiracPAMThe Principles of Quantum Mechanics1958OxfordClaredon Press10.1063/1.3062610 Klauder, J.R.: Using affine quantization to analyze non-renormalizable scalar fields and the quantization of Einstein’s gravity. J. High Energy Phys. Gravit. Cosmol. 6, 802 (2020) KlauderJRBeyond Conventional Quantization2000CambridgeCambridge University Press0956.81001 GoubaLAffine quantization on the half lineJ. High Energy Phys. Gravit. Cosmol.2021735210.4236/jhepgc.2021.71019 Fantoni, R., Klauder, J. R.: Monte Carlo evaluation of the continuum limit of the two-point function of two Euclidean Higgs real scalar fields subject to affine quantization. Phys. Rev. D (2021) arXiv:2107.08601 N Metropolis (2818_CR7) 1953; 1087 JR Klauder (2818_CR2) 2000 2818_CR4 2818_CR1 L Gouba (2818_CR10) 2021; 7 MH Kalos (2818_CR6) 2008 DM Ceperley (2818_CR8) 1995; 67 2818_CR12 R Fantoni (2818_CR5) 2021; 103 2818_CR9 PAM Dirac (2818_CR3) 1958 JR Klauder (2818_CR11) 2020; 6 |
| References_xml | – reference: MetropolisNRosenbluthAWRosenbluthMNTellerAMTellerEEquation of state calculations by fast computing machinesJ. Chem. Phys.19531087211431.65006 – reference: Klauder, J.R.: The benefits of affine quantization. J. High Energy Phys. Gravit. Cosmol. 6, 175 (2020) – reference: DiracPAMThe Principles of Quantum Mechanics1958OxfordClaredon Press10.1063/1.3062610 – reference: Fantoni, R.: Monte Carlo evaluation of the continuum limit of (ϕ12)3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi ^{12})_3$$\end{document}, J. Stat. Mech. 083102 (2021) – reference: KlauderJRBeyond Conventional Quantization2000CambridgeCambridge University Press0956.81001 – reference: KlauderJRAn ultralocal classical and quantum gravity theoryJ. High Energy Phys. Gravit. Cosmol.2020665610.4236/jhepgc.2020.64044 – reference: KalosMHWhitlockPAMonte Carlo Methods2008HobokenWiley10.1002/9783527626212 – reference: FantoniRKlauderJRAffine Quantization of (φ4)4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varphi ^{4})_4$$\end{document} Succeeds While Canonical Quantization FailsPhys. Rev. D20211030760132021PhRvD.103g6013F425993810.1103/PhysRevD.103.076013 – reference: CeperleyDMPath integrals in the theory of condensed heliumRev. Mod. Phys.1995672791995RvMP...67..279C10.1103/RevModPhys.67.279 – reference: Klauder, J.R.: Using affine quantization to analyze non-renormalizable scalar fields and the quantization of Einstein’s gravity. J. High Energy Phys. Gravit. Cosmol. 6, 802 (2020) – reference: GoubaLAffine quantization on the half lineJ. High Energy Phys. Gravit. Cosmol.2021735210.4236/jhepgc.2021.71019 – reference: Fantoni, R., Klauder, J. R.: Monte Carlo evaluation of the continuum limit of the two-point function of two Euclidean Higgs real scalar fields subject to affine quantization. Phys. Rev. D (2021) arXiv:2107.08601 – volume-title: Beyond Conventional Quantization year: 2000 ident: 2818_CR2 – ident: 2818_CR12 doi: 10.1007/s10955-021-02818-x – volume: 67 start-page: 279 year: 1995 ident: 2818_CR8 publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.67.279 – volume-title: Monte Carlo Methods year: 2008 ident: 2818_CR6 doi: 10.1002/9783527626212 – ident: 2818_CR9 doi: 10.4236/jhepgc.2020.64053 – volume: 103 start-page: 076013 year: 2021 ident: 2818_CR5 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.103.076013 – volume: 1087 start-page: 21 year: 1953 ident: 2818_CR7 publication-title: J. Chem. Phys. – ident: 2818_CR1 doi: 10.4236/jhepgc.2020.62014 – ident: 2818_CR4 doi: 10.1088/1742-5468/ac0f69 – volume: 7 start-page: 352 year: 2021 ident: 2818_CR10 publication-title: J. High Energy Phys. Gravit. Cosmol. doi: 10.4236/jhepgc.2021.71019 – volume: 6 start-page: 656 year: 2020 ident: 2818_CR11 publication-title: J. High Energy Phys. Gravit. Cosmol. doi: 10.4236/jhepgc.2020.64044 – volume-title: The Principles of Quantum Mechanics year: 1958 ident: 2818_CR3 doi: 10.1063/1.3062610 |
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| Title | Monte Carlo Evaluation of the Continuum Limit of the Two-Point Function of the Euclidean Free Real Scalar Field Subject to Affine Quantization |
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