统计场论 - 版本历史

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2022年6月6日 (一) 08:44 AvecSally

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Moonscar：Moved page from wikipedia:en:Statistical field theory (history)

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Moved page from wikipedia:en:Statistical field theory (history)

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In [[theoretical physics]], '''statistical field theory''' ('''SFT''') is a theoretical framework that describes [[phase transitions]].<ref>{{cite book |last1=Le Bellac |first1=Michel |title=Quantum and Statistical Field Theory |date=1991 |publisher=Clarendon Press |location=Oxford |isbn=978-0198539643}}</ref> It does not denote a single theory but encompasses many models, including for [[magnetism]], [[superconductivity]], [[superfluidity]],<ref>{{cite book |last1=Altland |first1=Alexander |last2=Simons |first2=Ben |title=Condensed Matter Field Theory |date=2010 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-76975-4 |edition=2nd}}</ref> [[topological phase transition]], [[wetting]]<ref>{{cite journal |last1=Rejmer |first1=K. |last2=Dietrich |first2=S. |last3=Napiórkowski |first3=M. |title=Filling transition for a wedge |journal=Phys. Rev. E |date=1999 |volume=60 |issue=4 |pages=4027–4042 |doi=10.1103/PhysRevE.60.4027|pmid=11970240 |arxiv=cond-mat/9812115 |bibcode=1999PhRvE..60.4027R |s2cid=23431707 }}</ref><ref>{{cite journal |last1=Parry |first1=A.O. |last2=Rascon |first2=C. |last3=Wood |first3=A.J. |title=Universality for 2D Wedge Wetting |journal=Phys. Rev. Lett. |date=1999 |volume=83 |issue=26 |pages=5535–5538 |doi=10.1103/PhysRevLett.83.5535|arxiv=cond-mat/9912388 |bibcode=1999PhRvL..83.5535P |s2cid=119364261 }}</ref> as well as non-equilibrium phase transitions.<ref>{{cite book |last1=Täuber |first1=Uwe |title=Critical Dynamics |date=2014 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-84223-5}}</ref> A SFT is any model in [[statistical mechanics]] where the [[Degrees of freedom (physics and chemistry)|degrees of freedom]] comprise a [[Field (physics)|field]] or fields. In other words, the [[Microstate (statistical mechanics)|microstates]] of the system are expressed through field configurations. It is closely related to [[quantum field theory]], which describes the [[quantum mechanics]] of fields, and shares with it many techniques, such as the [[path integral formulation]] and [[renormalization]].
If the system involves polymers, it is also known as [[polymer field theory]].

In theoretical physics, statistical field theory (SFT) is a theoretical framework that describes phase transitions. It does not denote a single theory but encompasses many models, including for magnetism, superconductivity, superfluidity, topological phase transition, wetting as well as non-equilibrium phase transitions. A SFT is any model in statistical mechanics where the degrees of freedom comprise a field or fields. In other words, the microstates of the system are expressed through field configurations. It is closely related to quantum field theory, which describes the quantum mechanics of fields, and shares with it many techniques, such as the path integral formulation and renormalization.
If the system involves polymers, it is also known as polymer field theory.

在理论物理学中，统计场论是描述相变的理论框架。它不表示一个单一的理论，但包括许多模型，包括磁性，超导现象，超流体，拓扑相变，润湿以及非平衡相变。一个 SFT 是任何一个统计力学的模型，其中自由度包含一个或多个领域。换句话说，系统的微观状态是通过场构型来表示的。它与量子场论密切相关，量子场论描述了场的量子力学，并与量子场论共享许多技术，如路径积分表述和重整化。如果这个系统包含聚合物，它也被称为高分子场论。

In fact, by performing a [[Wick rotation]] from [[Minkowski space]] to [[Euclidean space]], many results of statistical field theory can be applied directly to its quantum equivalent.{{citation needed|date=November 2018}} The [[Correlation function (quantum field theory)|correlation function]]s of a statistical field theory are called [[Schwinger function]]s, and their properties are described by the [[Osterwalder–Schrader axioms]].

In fact, by performing a Wick rotation from Minkowski space to Euclidean space, many results of statistical field theory can be applied directly to its quantum equivalent. The correlation functions of a statistical field theory are called Schwinger functions, and their properties are described by the Osterwalder–Schrader axioms.

实际上，通过执行从闵可夫斯基空间到欧氏空间的 Wick 旋转，统计场论的许多结果可以直接应用到它的量子等价物上。统计场论的相关函数称为 Schwinger 函数，其性质用 Osterwalder-Schrader 公理来描述。

Statistical field theories are widely used to describe systems in [[polymer physics]] or [[biophysics]], such as [[polymer]] films, nanostructured block [[copolymers]]<ref>{{cite journal |vauthors=Baeurle SA, Usami T, Gusev AA | title= A new multiscale modeling approach for the prediction of mechanical properties of [[polymer-based nanomaterials]] | journal=Polymer | year=2006 | volume=47 | pages=8604–8617 | doi=10.1016/j.polymer.2006.10.017 | issue= 26}}</ref> or [[polyelectrolyte]]s.<ref>{{cite journal |vauthors=Baeurle SA, Nogovitsin EA | title= Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts | journal=Polymer | year=2007 | volume=48 | pages=4883–4899 | doi=10.1016/j.polymer.2007.05.080 | issue= 16}}</ref>

Statistical field theories are widely used to describe systems in polymer physics or biophysics, such as polymer films, nanostructured block copolymers or polyelectrolytes.

统计场理论广泛用于描述聚合物物理或生物物理体系，如聚合物薄膜、纳米结构嵌段共聚物或聚电解质。

==Notes==
{{reflist}}

==References==
*{{cite book |title=Statistical Field Theory |volume=I, II |series=Cambridge Monographs on Mathematical Physics |first1=Claude |last1=Itzykson |first2=Jean-Michel |last2=Drouffe |publisher=Cambridge University Press |date=1991 |isbn=0-521-40806-7}} {{ISBN|0-521-40805-9}}
*{{cite book |first=Giorgio |last=Parisi |title=Statistical Field Theory |url=https://books.google.com/books?id=bivTswEACAAJ |date=1998 |publisher=Perseus Books |isbn=978-0-7382-0051-4 |series=Advanced Book Classics}}
*{{cite book |title=The P(φ)<sub>2</sub> Euclidean (quantum) field theory |first=Barry |last=Simon |publisher=Princeton University Press |date=1974 |isbn=0-691-08144-1}}
*{{cite book |title=Quantum Physics: A Functional Integral Point of View |first1=James |last1=Glimm |first2=Arthur |last2=Jaffe |publisher=Springer |edition=2nd |date=1987 |isbn=0-387-96477-0}}

*
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*
*

==References==

*

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*

==External links==
*[https://web.archive.org/web/20060925105340/http://www.gursey.gov.tr/~mgh/rg2006/problemsets.html Problems in Statistical Field Theory]
*[https://web.archive.org/web/20090107204013/http://www-dick.chemie.uni-regensburg.de/group/stephan_baeurle/ Particle and Polymer Field Theory Group]
{{Statistical mechanics topics}}
{{Industrial and applied mathematics}}

*Problems in Statistical Field Theory
*Particle and Polymer Field Theory Group

= = = 外部链接 = =
* 统计场论中的问题
* 粒子和高分子场论群

[[Category:Applied mathematics]]
[[Category:Mathematical physics]]
[[Category:Statistical field theories|*]]

Category:Applied mathematics
Category:Mathematical physics
*

类别: 应用数学类别: 数学物理 *

{{physics-stub}}

<noinclude>

<small>This page was moved from [[wikipedia:en:Statistical field theory]]. Its edit history can be viewed at [[统计场论/edithistory]]</small></noinclude>

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-此词条暂由彩云小译翻译，翻译字数共209，未经人工整理和审校，带来阅读不便，请见谅。
+在理论物理学中，统计场理论（SFT）是一个描述相变的理论框架。它并不表示一个单一的理论，而是包含了许多模型，包括用于磁性、超导性、超流性、拓扑相变、湿化以及非平衡相变。SFT是统计力学的任何模型，其中自由度由一个或多个场组成。换句话说，系统的微观状态是通过场的配置来表达的。它与描述场的量子力学的量子场理论密切相关，并与它共享许多技术，如路径积分公式和重整化。如果该系统涉及聚合物，它也被称为高分子场论。
-In [[theoretical physics]], '''statistical field theory''' ('''SFT''') is a theoretical framework that describes [[phase transitions]].<ref>{{cite book |last1=Le Bellac |first1=Michel |title=Quantum and Statistical Field Theory |date=1991 |publisher=Clarendon Press |location=Oxford |isbn=978-0198539643}}</ref> It does not denote a single theory but encompasses many models, including for [[magnetism]], [[superconductivity]], [[superfluidity]],<ref>{{cite book |last1=Altland |first1=Alexander |last2=Simons |first2=Ben |title=Condensed Matter Field Theory |date=2010 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-76975-4 |edition=2nd}}</ref> [[topological phase transition]], [[wetting]]<ref>{{cite journal |last1=Rejmer |first1=K. |last2=Dietrich |first2=S. |last3=Napiórkowski |first3=M. |title=Filling transition for a wedge |journal=Phys. Rev. E |date=1999 |volume=60 |issue=4 |pages=4027–4042 |doi=10.1103/PhysRevE.60.4027|pmid=11970240 |arxiv=cond-mat/9812115 |bibcode=1999PhRvE..60.4027R |s2cid=23431707 }}</ref><ref>{{cite journal |last1=Parry |first1=A.O. |last2=Rascon |first2=C. |last3=Wood |first3=A.J. |title=Universality for 2D Wedge Wetting |journal=Phys. Rev. Lett. |date=1999 |volume=83 |issue=26 |pages=5535–5538 |doi=10.1103/PhysRevLett.83.5535|arxiv=cond-mat/9912388 |bibcode=1999PhRvL..83.5535P |s2cid=119364261 }}</ref> as well as non-equilibrium phase transitions.<ref>{{cite book |last1=Täuber |first1=Uwe |title=Critical Dynamics |date=2014 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-84223-5}}</ref> A SFT is any model in [[statistical mechanics]] where the [[Degrees of freedom (physics and chemistry)|degrees of freedom]] comprise a [[Field (physics)|field]] or fields. In other words, the [[Microstate (statistical mechanics)|microstates]] of the system are expressed through field configurations. It is closely related to [[quantum field theory]], which describes the [[quantum mechanics]] of fields, and shares with it many techniques, such as the [[path integral formulation]] and [[renormalization]].
+事实上，通过进行从闵可夫斯基空间到欧几里得空间的Wick旋转，统计场论的许多结果可以直接应用于其量子等价物。统计场论的相关函数被称为Schwinger函数，其属性由Osterwalder-Schrader 公理描述。
-In theoretical physics, statistical field theory (SFT) is a theoretical framework that describes phase transitions. It does not denote a single theory but encompasses many models, including for magnetism, superconductivity, superfluidity, topological phase transition, wetting as well as non-equilibrium phase transitions. A SFT is any model in statistical mechanics where the degrees of freedom comprise a field or fields. In other words, the microstates of the system are expressed through field configurations. It is closely related to quantum field theory, which describes the quantum mechanics of fields, and shares with it many techniques, such as the path integral formulation and renormalization.
+统计场理论被广泛用于描述高分子物理学或生物物理学中的系统，如聚合物薄膜、纳米结构的嵌段共聚物或聚电解质。
 ==Notes==
@@ 第33行： / 第17行： @@
+*
+*
+*
+*

@@ 第1行： / 第1行： @@
-在理论物理学中，统计场理论（SFT）是一个描述相变的理论框架。它并不表示一个单一的理论，而是包含了许多模型，包括用于磁性、超导性、超流性、拓扑相变、湿化以及非平衡相变。SFT是统计力学的任何模型，其中自由度由一个或多个场组成。换句话说，系统的微观状态是通过场的配置来表达的。它与描述场的量子力学的量子场理论密切相关，并与它共享许多技术，如路径积分公式和重整化。如果该系统涉及聚合物，它也被称为高分子场论。
+在理论物理学[https://wiki.swarma.org/index.php/Theoretical_physics Theoretical Physics]中，统计场理论'''Statistical Field Theory'''（SFT）是一个描述相变<ref>{{cite book |last1=Le Bellac |first1=Michel |title=Quantum and Statistical Field Theory |date=1991 |publisher=Clarendon Press |location=Oxford |isbn=978-0198539643}}</ref>的理论框架。它并不表示一个单一的理论，而是包含了许多模型，包括用于磁性、超导性、超流性<ref>{{cite book |last1=Altland |first1=Alexander |last2=Simons |first2=Ben |title=Condensed Matter Field Theory |date=2010 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-76975-4 |edition=2nd}}</ref>、拓扑相变、湿化<ref>{{cite journal |last1=Rejmer |first1=K. |last2=Dietrich |first2=S. |last3=Napiórkowski |first3=M. |title=Filling transition for a wedge |journal=Phys. Rev. E |date=1999 |volume=60 |issue=4 |pages=4027–4042 |doi=10.1103/PhysRevE.60.4027|pmid=11970240 |arxiv=cond-mat/9812115 |bibcode=1999PhRvE..60.4027R |s2cid=23431707 }}</ref><ref>{{cite journal |last1=Parry |first1=A.O. |last2=Rascon |first2=C. |last3=Wood |first3=A.J. |title=Universality for 2D Wedge Wetting |journal=Phys. Rev. Lett. |date=1999 |volume=83 |issue=26 |pages=5535–5538 |doi=10.1103/PhysRevLett.83.5535|arxiv=cond-mat/9912388 |bibcode=1999PhRvL..83.5535P |s2cid=119364261 }}</ref>以及非平衡相变<ref>{{cite book |last1=Täuber |first1=Uwe |title=Critical Dynamics |date=2014 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-84223-5}}</ref>。统计场理论SFT是统计力学的任何模型，其中自由度由一个或多个场组成。换句话说，系统的微观状态是通过场的配置来表达的。它与描述场的量子力学的量子场理论密切相关，并与它共享许多技术，如路径积分公式和重整化。如果该系统涉及聚合物，它也被称为高分子场论。
-事实上，通过进行从闵可夫斯基空间到欧几里得空间的Wick旋转，统计场论的许多结果可以直接应用于其量子等价物。统计场论的相关函数被称为Schwinger函数，其属性由Osterwalder-Schrader 公理描述。
+事实上，通过进行从闵可夫斯基空间[https://wiki.swarma.org/index.php/Minkowski_space Minkowski space]到欧几里得空间[https://wiki.swarma.org/index.php/Euclidean_space Euclidean space]的Wick旋转[https://wiki.swarma.org/index.php/Wick_rotation Wick Rotation]，统计场论的许多结果可以直接应用于其量子等价物。统计场论的相关函数被称为Schwinger函数[https://wiki.swarma.org/index.php/Schwinger_function Schwinger function]s，其属性由Osterwalder-Schrader 公理描述。
-统计场理论被广泛用于描述高分子物理学或生物物理学中的系统，如聚合物薄膜、纳米结构的嵌段共聚物或聚电解质。
+统计场理论被广泛用于描述高分子物理学或生物物理学中的系统，如聚合物薄膜、纳米结构的嵌段共聚物<ref>{{cite journal |vauthors=Baeurle SA, Usami T, Gusev AA | title= A new multiscale modeling approach for the prediction of mechanical properties of [[polymer-based nanomaterials]] | journal=Polymer | year=2006 | volume=47 | pages=8604–8617 | doi=10.1016/j.polymer.2006.10.017 | issue= 26}}</ref>或聚电解质<ref>{{cite journal |vauthors=Baeurle SA, Nogovitsin EA | title= Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts | journal=Polymer | year=2007 | volume=48 | pages=4883–4899 | doi=10.1016/j.polymer.2007.05.080 | issue= 16}}</ref>。
-==Notes==
+==参考文献==
 {{reflist}}
-==References==
+==参考资料==
-*{{cite book |title=Statistical Field Theory |volume=I, II |series=Cambridge Monographs on Mathematical Physics |first1=Claude |last1=Itzykson  |first2=Jean-Michel |last2=Drouffe |publisher=Cambridge University Press |date=1991 |isbn=0-521-40806-7}} {{ISBN|0-521-40805-9}}
+*{{cite book |title=Statistical Field Theory |volume=I, II |series=Cambridge Monographs on Mathematical Physics |first1=Claude |last1=Itzykson  |first2=Jean-Michel |last2=Drouffe |publisher=Cambridge University Press |date=1991 |isbn=0-521-40806-7}}
 *{{cite book |first=Giorgio |last=Parisi |title=Statistical Field Theory |url=https://books.google.com/books?id=bivTswEACAAJ |date=1998 |publisher=Perseus Books |isbn=978-0-7382-0051-4 |series=Advanced Book Classics}}
 *{{cite book |title=The P(φ)<sub>2</sub> Euclidean (quantum) field theory |first=Barry |last=Simon |publisher=Princeton University Press |date=1974 |isbn=0-691-08144-1}}
 *{{cite book |title=Quantum Physics: A Functional Integral Point of View |first1=James |last1=Glimm |first2=Arthur |last2=Jaffe |publisher=Springer |edition=2nd |date=1987 |isbn=0-387-96477-0}}
+*
+*
+*
 *[https://web.archive.org/web/20060925105340/http://www.gursey.gov.tr/~mgh/rg2006/problemsets.html Problems in Statistical Field Theory]
-*[https://web.archive.org/web/20090107204013/http://www-dick.chemie.uni-regensburg.de/group/stephan_baeurle/ Particle and Polymer Field Theory Group]
+*[https://web.archive.org/web/20090107204013/http://www-dick.chemie.uni-regensburg.de/group/stephan_baeurle/ Particle and Polymer Field Theory Group]<br />
-{{Statistical mechanics topics}}
+[[Category:Applied mathematics]]
-{{Industrial and applied mathematics}}
+[[Category:Mathematical physics]]
-*Problems in Statistical Field Theory
+==编者推荐==
-*Particle and Polymer Field Theory Group
+===集智课程===
-= = = 外部链接 = =
+[[文件:循环神经网络的动力学平均场理论.png|缩略图|[https://swarma.org/?p=33644 循环神经网络的动力学平均场理论]]]
-Category:Applied mathematics
+[https://swarma.org/?p=33644 循环神经网络的动力学平均场理论]
-类别: 应用数学类别: 数学物理 *
+随着电生理学、网络建模、机器学习、统计物理、类脑计算等多种技术方法的发展，我们对大脑神经元相互作用机理与连接机制，对意识、语言、情绪、记忆、社交等功能的认识逐渐深入，大脑复杂系统的谜底正在被揭开。为了促进神经科学、系统科学、计算机科学等领域研究者的交流合作，我们发起了【神经动力学模型读书会】，本次分享属于【神经动力学模型读书会】第三期：循环神经网络的动力学平均场理论。
-{{physics-stub}}
+鸟类的飞行受空气动力学和生物力学约束，因此鸟群中个体的速度涨落是有限的。然而速度涨落的空间相关性是无标度的，即作用范围涉及整个鸟群，这一性质与系统对外界扰动的集体响应能力有关。无标度相关性和有限的速度涨落，为控制个体速度的机制施加了相矛盾的约束：如果提升相关性的因素会放大速度涨落，反之亦然。近日发表于 ''Nature Communications'' 一项最新研究采用统计场论方法，提出忽略小涨落且强烈抑制大涨落的边际速度约束，能够调和无标度相关性和符合生理的群体速度。本文将这些理论预测与规模跨越两个以上数量级的椋鸟群实地实验数据对比，证实了边际速度约束的有效性。
-<noinclude>
+----本中文词条由[[用户:Bingyu Jiang|Bingyu Jiang]]翻译，[https://wiki.swarma.org/index.php/%E7%94%A8%E6%88%B7:AvecSally AvecSally]编辑，如有问题，欢迎在讨论页面留言。
 [[Category:待整理页面]]