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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}}
*
*
*
*
==References==
*
*
*
*
==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>
[[Category:待整理页面]]
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}}
*
*
*
*
==References==
*
*
*
*
==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>
[[Category:待整理页面]]