Coleman–Weinberg potential (original) (raw)
양자장론에서 콜먼 와인버그 모형(영어: Coleman–Weinberg model)은 으로 인하여 자발 대칭 깨짐이 일어나는 스칼라 양자 전기역학 모형이다.
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| dbo:abstract | The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is where the scalar field is complex, is the electromagnetic field tensor, and the covariant derivative containing the electric charge of the electromagnetic field. Assume that is nonnegative. Then if the mass term is tachyonic, there is a spontaneous breaking of the gauge symmetry at low energies, a variant of the Higgs mechanism. On the other hand, if the squared mass is positive, the vacuum expectation of the field is zero. At the classical level the latter is true also if . However, as was shown by Sidney Coleman and Erick Weinberg, even if the renormalized mass is zero, spontaneous symmetry breaking still happens due to the radiative corrections (this introduces a mass scale into a classically conformal theory - model have a conformal anomaly). The same can happen in other gauge theories. In the broken phase the fluctuations of the scalar field will manifest themselves as a naturally light Higgs boson, as a matter of fact even too light to explain the electroweak symmetry breaking in the minimal model - much lighter than vector bosons. There are non-minimal models that give a more realistic scenarios. Also the variations of this mechanism were proposed for the hypothetical spontaneously broken symmetries including supersymmetry. Equivalently one may say that the model possesses a first-order phase transition as a function of . The model is the four-dimensional analog of the three-dimensional Ginzburg–Landau theory used to explain the properties of superconductors near the phase transition. The three-dimensional version of the Coleman–Weinberg model governs the superconducting phase transition which can be both first- and second-order, depending on the ratio of the Ginzburg–Landau parameter , with a tricritical point near which separates type I from type II superconductivity.Historically, the order of the superconducting phase transition was debated for a long time since the temperatureinterval where fluctuations are large is extremely small.The question was finally settledin 1982. If the Ginzburg–Landau parameter that distinguishes type-I and type-II superconductors (see also here)is large enough, vortex fluctuations becomes important which drive the transition to second order.The tricritical point lies atroughly, i.e., slightly below the value where type-I goes over into type-II superconductor.The prediction was confirmed in 2002 by Monte Carlo computer simulations. (en) Der Coleman-Weinberg-Mechanismus (nach den US-amerikanischen Physikern Sidney Coleman und Erick Weinberg) ist ein Mechanismus zur Erklärung spontaner Symmetriebrechung in Quantenfeldtheorien. Der Coleman-Weinberg-Mechanismus benötigt dabei – im Gegensatz zum Higgs-Mechanismus – nicht die Einführung zusätzlicher freier Parameter der Theorie; stattdessen basiert er auf Quanteneffekten aus Korrekturen höherer Ordnung in der Störungstheorie. Der Coleman-Weinberg-Mechanismus ist ein Beispiel, wie eine marginale Kopplung einen bedeutenden Einfluss auf die gesamte Theorie erhält. Die spontane Symmetriebrechung des Coleman-Weinberg-Mechanismus sagt für das Verhältnis zwischen Skalarboson und massivem Vektorboson folgendes Verhältnis voraus: Dabei ist die Feinstrukturkonstante. Nach dem Standardmodell ist der Coleman-Weinberg-Mechanismus nicht etabliert; dieses gibt dem Higgs-Mechanismus den Vorzug. (de) El modelo de Coleman–Weinberg representa un modelo de la electrodinámica cuántica de un campo escalar en cuatro dimensiones. El lagrangiano para el modelo es donde el campo escalar es complejo, es el tensor de campo electromagnético, y la derivada covariante que contiene el acoplamiento con el campo electromagnético. Se asume que es no-negativo. Entonces si el término de masa es taquiónico , hay una ruptura espontánea de simetría gauge a energías bajas, una variante del mecanismo de Higgs. Por otro lado, si la masa al cuadrado es positiva , el valor esperado en el vacío del campo es cero. En el nivel clásico, esto último es cierto también si . Aun así, como demostraron Sidney Coleman y incluso si la masa renormalizada es cero, existe ruptura espontánea de la simetría debido a las correcciones radiativas (esto introduce una escala de masa a una teoría conforme clásicamente - el modelo tiene una anomalía conforme). Lo mismo puede pasar en otras teorías gauge. En la fase rota las fluctuaciones del campo escalar se manifestarán como bosones de Higgs naturalmente ligeros, de hecho incluso demasiado ligeros para explicar la ruptura de simetría electrodébil en el modelo mínimo - mucho más ligeros que los bosones vectoriales. Hay modelos no mínimos que dan unos escenarios más realistas. También se propusieron variaciones de este mecanismo para hipotéticas rupturas espontáneas de la simetría incluyendo supersimetría. Equivalentemente se puede decir que el modelo posee una transición de fase de primer orden como función de . El modelo es el equivalente en cuatro dimensiones de la teoría de Ginzburg–Landau empleada para explicar las propiedades de los superconductores cerca de la transición de fase. (es) 양자장론에서 콜먼 와인버그 모형(영어: Coleman–Weinberg model)은 으로 인하여 자발 대칭 깨짐이 일어나는 스칼라 양자 전기역학 모형이다. (ko) 科尔曼–温伯格模型用于表示四维时空中一个标量场的量子电动力学。这个模型的拉格朗日量为： 其中是复标量场，是电磁场张量，是相应的协变导数。 假设是非负的（一般而言，为了势函数有下界，必须为非负的）。 如果质量项是“超光速”的,即 ，那么在低能量尺度，理论中存在规范对称性的自发破缺，即所谓的希格斯机制。 另外如果质量的平方是正的， ，是零。 在经典理论中，如果 < ，这样的结论已然成立。然而，正如西德尼 科尔曼 和 所提出的， 即使重整化的质量为零，由于有辐射修正，自发性对称性破缺仍然会发生(这将在一个经典的共形理论中引入一个质量尺度，这样的理论具有了共形反常)。 (zh) |
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| rdfs:comment | 양자장론에서 콜먼 와인버그 모형(영어: Coleman–Weinberg model)은 으로 인하여 자발 대칭 깨짐이 일어나는 스칼라 양자 전기역학 모형이다. (ko) 科尔曼–温伯格模型用于表示四维时空中一个标量场的量子电动力学。这个模型的拉格朗日量为： 其中是复标量场，是电磁场张量，是相应的协变导数。 假设是非负的（一般而言，为了势函数有下界，必须为非负的）。 如果质量项是“超光速”的,即 ，那么在低能量尺度，理论中存在规范对称性的自发破缺，即所谓的希格斯机制。 另外如果质量的平方是正的， ，是零。 在经典理论中，如果 < ，这样的结论已然成立。然而，正如西德尼 科尔曼 和 所提出的， 即使重整化的质量为零，由于有辐射修正，自发性对称性破缺仍然会发生(这将在一个经典的共形理论中引入一个质量尺度，这样的理论具有了共形反常)。 (zh) The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is where the scalar field is complex, is the electromagnetic field tensor, and the covariant derivative containing the electric charge of the electromagnetic field. Equivalently one may say that the model possesses a first-order phase transition as a function of . The model is the four-dimensional analog of the three-dimensional Ginzburg–Landau theory used to explain the properties of superconductors near the phase transition. (en) Der Coleman-Weinberg-Mechanismus (nach den US-amerikanischen Physikern Sidney Coleman und Erick Weinberg) ist ein Mechanismus zur Erklärung spontaner Symmetriebrechung in Quantenfeldtheorien. Der Coleman-Weinberg-Mechanismus benötigt dabei – im Gegensatz zum Higgs-Mechanismus – nicht die Einführung zusätzlicher freier Parameter der Theorie; stattdessen basiert er auf Quanteneffekten aus Korrekturen höherer Ordnung in der Störungstheorie. Der Coleman-Weinberg-Mechanismus ist ein Beispiel, wie eine marginale Kopplung einen bedeutenden Einfluss auf die gesamte Theorie erhält. (de) El modelo de Coleman–Weinberg representa un modelo de la electrodinámica cuántica de un campo escalar en cuatro dimensiones. El lagrangiano para el modelo es donde el campo escalar es complejo, es el tensor de campo electromagnético, y la derivada covariante que contiene el acoplamiento con el campo electromagnético. (es) |
| rdfs:label | Coleman-Weinberg-Mechanismus (de) Mecanismo de Coleman-Weinberg (es) Coleman–Weinberg potential (en) 콜먼-와인버그 모형 (ko) 科尔曼-温伯格模型 (zh) |
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