Gauge fixing (original) (raw)
Калибро́вка ве́кторного потенциа́ла — наложение дополнительных условий, позволяющих однозначно вычислить векторный потенциал электромагнитного поля при решении тех или иных физических задач. Налагаемые условия являются искусственными и служат для упрощения математических выкладок. Наиболее широкое распространение получили калибровка Кулона и калибровка Лоренца, но существуют и применяются и другие калибровки.
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| dbo:abstract | In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom. Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them). Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present. (en) Na física de teorias de gauge, fixação de gauge ou fixação de calibre (também chamada escolha de um gauge) denota um procedimento matemático para a cópia com graus de liberdade redundantes em campos variáveis. Por definição, uma teoria de gauge representa fisicamente cada configuração distinta do sistema como uma classe equivalente de configurações de detalhadas. Qualquer duas configurações detalhadas na mesma classe equivalente são relacionadas por uma transformação de gauge, equivalente a uma transformação de simetria ao longo dos eixos geométricos (não físicos) no espaço de configuração. A maioria das predições físicas quantitativas de uma teoria de gauge podem somente ser obtidas sob uma coerente supressão ou ignorando estes graus de liberdade não físicos. Embora os eixos não físicos no espaço de configurações detalhadas sejam uma propriedade fundamental do modelo físico, não existe um conjunto especial de direções "perpendiculares" a eles. Desde que existe uma enorme quantidade de liberdade envolvida na tomada de uma "seção transversal" representando cada configuração física por uma configuração detalhada particular (ou mesmo de uma distribuição ponderada delas). Arbitrárias fixações de gauge podem simplificar cálculos imensamente, mas tornam-se progressivamente mais difíceis à medida que o modelo se torna mais realista; sua aplicação na teoria quântica de campos é trabalhosa com complicações relacionadas à renormalização, especialmente quando a computação é continuada a mais altas ordens. Historicamente, a busca por procedimentos de fixação de gauge logicamente consistentes e tratáveis computacionalmente, e esforços para demonstrar sua equivalência em face de uma confusa variedade de dificuldades técnicas, tem sido um principal condutor da física matemática do século XIX ao presente. (pt) Калибро́вка ве́кторного потенциа́ла — наложение дополнительных условий, позволяющих однозначно вычислить векторный потенциал электромагнитного поля при решении тех или иных физических задач. Налагаемые условия являются искусственными и служат для упрощения математических выкладок. Наиболее широкое распространение получили калибровка Кулона и калибровка Лоренца, но существуют и применяются и другие калибровки. (ru) 库仑规范（Coulomb gauge）是一种横场条件，定义为 。 标量势φ和矢量势A对电磁场的确定不是唯一的，有可能对它们引进适当的限制条件。 在库仑规范下，时变电磁场情形下，标量势φ由方程确定。这是瞬时的库仑势方程，库仑规范的名称由此而得。 在推导磁矢势时候可以借助来得到 。 (zh) Калібрува́ння ве́кторного потенціа́лу — накладення додаткових умов, що дозволяють однозначно обчислити векторний потенціал електромагнітного поля під час розв'язування тих чи інших фізичних задач. Накладені умови є штучними і покликані спростити математичні перетворення. Найбільшого поширення набули калібрування Кулона та калібрування Лоренца, але існують і застосовуються й інші калібрування. (uk) |
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| rdfs:comment | Калибро́вка ве́кторного потенциа́ла — наложение дополнительных условий, позволяющих однозначно вычислить векторный потенциал электромагнитного поля при решении тех или иных физических задач. Налагаемые условия являются искусственными и служат для упрощения математических выкладок. Наиболее широкое распространение получили калибровка Кулона и калибровка Лоренца, но существуют и применяются и другие калибровки. (ru) 库仑规范（Coulomb gauge）是一种横场条件，定义为 。 标量势φ和矢量势A对电磁场的确定不是唯一的，有可能对它们引进适当的限制条件。 在库仑规范下，时变电磁场情形下，标量势φ由方程确定。这是瞬时的库仑势方程，库仑规范的名称由此而得。 在推导磁矢势时候可以借助来得到 。 (zh) Калібрува́ння ве́кторного потенціа́лу — накладення додаткових умов, що дозволяють однозначно обчислити векторний потенціал електромагнітного поля під час розв'язування тих чи інших фізичних задач. Накладені умови є штучними і покликані спростити математичні перетворення. Найбільшого поширення набули калібрування Кулона та калібрування Лоренца, але існують і застосовуються й інші калібрування. (uk) In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom. (en) Na física de teorias de gauge, fixação de gauge ou fixação de calibre (também chamada escolha de um gauge) denota um procedimento matemático para a cópia com graus de liberdade redundantes em campos variáveis. Por definição, uma teoria de gauge representa fisicamente cada configuração distinta do sistema como uma classe equivalente de configurações de detalhadas. Qualquer duas configurações detalhadas na mesma classe equivalente são relacionadas por uma transformação de gauge, equivalente a uma transformação de simetria ao longo dos eixos geométricos (não físicos) no espaço de configuração. A maioria das predições físicas quantitativas de uma teoria de gauge podem somente ser obtidas sob uma coerente supressão ou ignorando estes graus de liberdade não físicos. (pt) |
| rdfs:label | Gauge fixing (en) Fixação de gauge (pt) Калибровка векторного потенциала (ru) 規範固定 (zh) Калібрування векторного потенціалу (uk) |
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