BRST quantization (original) (raw)
Die Becchi-Rouet-Stora-Tyutin-Symmetrie, kurz BRST-Symmetrie, teilweise auch nur Becchi-Rouet-Stora-Symmetrie (BRS-Symmetrie), nach Carlo Becchi, Alain Rouet, Raymond Stora und Igor Tyutin, ist eine Symmetrie in der Quantenfeldtheorie, die noch vorhanden ist, wenn die Eichung des Quantenfeldes bereits festgelegt wurde und das Quantenfeld dadurch nicht mehr eichsymmetrisch ist. Dies wird ermöglicht, indem die BRST-Symmetrie zusätzlich zur ursprünglichen Eichsymmetrie die Existenz der durch die Eichung entstehenden unphysikalischen Faddejew-Popow-Geister berücksichtigt und die Symmetrie auf der Basis von antikommutierenden Graßmann-Zahlen aufgebaut ist.
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| dbo:abstract | Die Becchi-Rouet-Stora-Tyutin-Symmetrie, kurz BRST-Symmetrie, teilweise auch nur Becchi-Rouet-Stora-Symmetrie (BRS-Symmetrie), nach Carlo Becchi, Alain Rouet, Raymond Stora und Igor Tyutin, ist eine Symmetrie in der Quantenfeldtheorie, die noch vorhanden ist, wenn die Eichung des Quantenfeldes bereits festgelegt wurde und das Quantenfeld dadurch nicht mehr eichsymmetrisch ist. Dies wird ermöglicht, indem die BRST-Symmetrie zusätzlich zur ursprünglichen Eichsymmetrie die Existenz der durch die Eichung entstehenden unphysikalischen Faddejew-Popow-Geister berücksichtigt und die Symmetrie auf der Basis von antikommutierenden Graßmann-Zahlen aufgebaut ist. (de) In theoretical physics, the BRST formalism, or BRST quantization (where the BRST refers to the last names of Carlo Becchi, , Raymond Stora and Igor Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier quantum field theory (QFT) frameworks resembled "prescriptions" or "heuristics" more than proofs, especially in non-abelian QFT, where the use of "ghost fields" with superficially bizarre properties is almost unavoidable for technical reasons related to renormalization and anomaly cancellation. The BRST global supersymmetry introduced in the mid-1970s was quickly understood to rationalize the introduction of these Faddeev–Popov ghosts and their exclusion from "physical" asymptotic states when performing QFT calculations. Crucially, this symmetry of the path integral is preserved in loop order, and thus prevents introduction of counterterms which might spoil renormalizability of gauge theories. Work by other authors a few years later related the BRST operator to the existence of a rigorous alternative to path integrals when quantizing a gauge theory. Only in the late 1980s, when QFT was reformulated in fiber bundle language for application to problems in the topology of low-dimensional manifolds (topological quantum field theory), did it become apparent that the BRST "transformation" is fundamentally geometrical in character. In this light, "BRST quantization" becomes more than an alternate way to arrive at anomaly-cancelling ghosts. It is a different perspective on what the ghost fields represent, why the Faddeev–Popov method works, and how it is related to the use of Hamiltonian mechanics to construct a perturbative framework. The relationship between gauge invariance and "BRST invariance" forces the choice of a Hamiltonian system whose states are composed of "particles" according to the rules familiar from the canonical quantization formalism. This esoteric consistency condition therefore comes quite close to explaining how quanta and fermions arise in physics to begin with. In certain cases, notably gravity and supergravity, BRST must be superseded by a more general formalism, the Batalin–Vilkovisky formalism. (en) BRST 양자화(영어: BRST quantization) 또는 베키-루에-스토라-튜틴 양자화(영어: Becchi–Rouet–Stora–Tyutin quantization)는 게이지 이론을 양자화하는 한 방법이다. 게이지 이론은 비물리적인 대칭(게이지 대칭)을 지녀 그냥 양자화하기 어렵다. 게이지 대칭을 무시하고 그냥 양자화하면 그 힐베르트 공간이 양의 정부호의 내적을 얻지 못한다. 따라서 상태공간에 차수(grading)를 붙이고 코호몰로지를 만들어 물리적 힐베르트 공간을 얻는다. (ko) Метод квантования Бекки — Руэ́ — Стора́ — Тютина (BRST-квантование) — метод теоретической физики, использующий строгий подход к квантованию теории поля при наличии калибровочной симметрии. Назван по именам (англ. Carlo Becchi), Алена Руэ (Alain Rouet), (фр. Raymond Stora) и Игоря Тютина. Правила квантования в ранних методах квантовой теории поля в большей степени были набором практических эвристик («рецептов»), нежели строгой системой. Особенно это касается случая , где использование «духов Фаддеева — Попова» с причудливыми свойствами просто необходимо по некоторым техническим причинам, связанным с ренормализацией и некорректным сокращением. BRST-суперсимметрия была изобретена в середине 1970-х и довольно быстро воспринята сообществом как способ строгого обоснования для введения духов Фаддеева — Попова и их исключения из физических асимптотик при вычислениях. Несколько лет спустя в работе другого автора[уточнить] была показано, что BRST-оператор свидетельствует о существовании формальной альтернативы интеграла по путям при квантовании калибровочной теории. Только в конце 1980-х готов, когда квантовая теория поля была сформулирована в терминах для возможности решения топологических проблем многообразий низкой размерности (теория Дональдсона), стало очевидно, что по своему характеру BRST-преобразование является фундаментально геометрическим. В таком свете «BRST-квантование» становится не просто способом добиться аномально сокращающихся гостов[уточнить]. Это другой взгляд на то, что собой представляют поля-духи, почему справедлив метод Фаддеева — Попова и как он связан с использованием гамильтоновой механики при конструировании модели возмущений. Соотношение между калибровочной инвариантностью и «BRST-инвариантностью» ограничивает выбор гамильтоновых систем, чьи состояния состоят из «частиц» в соответствии с правилами канонического квантования. Эта неявная согласованность подходит довольно близко к объяснению, откуда в физике появляются кванты и фермионы. В определенных случаях, в частности в теориях гравитации и супергравитации, BRST-квантование должно быть заменено более общим формализмом . (ru) 在理論物理學中，BRST量子化是指以較嚴格的數學方式、藉由規範對稱性以量子化場論，它以卡洛·贝基（Becchi）、阿兰·鲁埃（Rouet）、雷蒙·斯托拉（Stora）和伊戈尔·秋京（Tyutin）的首字母命名。在早期量子場論中，特別是，其中的「鬼場」幾乎都是以重整化和的方式處理。 70年代中期推出的BRST超對稱對量子場論進行計算時，合理引入法捷耶夫-波波夫鬼粒子，並從物理漸近狀態將其排除在外。至關重要的是，路徑積分得以防止引入可能破壞規範理論的項目。直到數十年後，物理學家才以BRST替代路徑積分的存在。 在20世紀80年代末，當量子場論得以解決低維流形拓撲結構的問題，BRST量子化變得比在利用以反常抵消解決鬼場的方法更有效。這種修改原始作用量，添加進去一個額外的場（鬼場）並打破規範對稱性的方法，即被稱作「法捷耶夫-波波夫方法」。至於規範不變性和BRST不變性之間的關係，使得哈密頓系統的狀態由粒子的規範量子化選擇。此外，在某些情況下，特別是重力和超引力，BRST必須由更一般的形式，例如以巴塔林-維爾可維斯基代數取代。 (zh) |
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| rdfs:comment | Die Becchi-Rouet-Stora-Tyutin-Symmetrie, kurz BRST-Symmetrie, teilweise auch nur Becchi-Rouet-Stora-Symmetrie (BRS-Symmetrie), nach Carlo Becchi, Alain Rouet, Raymond Stora und Igor Tyutin, ist eine Symmetrie in der Quantenfeldtheorie, die noch vorhanden ist, wenn die Eichung des Quantenfeldes bereits festgelegt wurde und das Quantenfeld dadurch nicht mehr eichsymmetrisch ist. Dies wird ermöglicht, indem die BRST-Symmetrie zusätzlich zur ursprünglichen Eichsymmetrie die Existenz der durch die Eichung entstehenden unphysikalischen Faddejew-Popow-Geister berücksichtigt und die Symmetrie auf der Basis von antikommutierenden Graßmann-Zahlen aufgebaut ist. (de) BRST 양자화(영어: BRST quantization) 또는 베키-루에-스토라-튜틴 양자화(영어: Becchi–Rouet–Stora–Tyutin quantization)는 게이지 이론을 양자화하는 한 방법이다. 게이지 이론은 비물리적인 대칭(게이지 대칭)을 지녀 그냥 양자화하기 어렵다. 게이지 대칭을 무시하고 그냥 양자화하면 그 힐베르트 공간이 양의 정부호의 내적을 얻지 못한다. 따라서 상태공간에 차수(grading)를 붙이고 코호몰로지를 만들어 물리적 힐베르트 공간을 얻는다. (ko) 在理論物理學中，BRST量子化是指以較嚴格的數學方式、藉由規範對稱性以量子化場論，它以卡洛·贝基（Becchi）、阿兰·鲁埃（Rouet）、雷蒙·斯托拉（Stora）和伊戈尔·秋京（Tyutin）的首字母命名。在早期量子場論中，特別是，其中的「鬼場」幾乎都是以重整化和的方式處理。 70年代中期推出的BRST超對稱對量子場論進行計算時，合理引入法捷耶夫-波波夫鬼粒子，並從物理漸近狀態將其排除在外。至關重要的是，路徑積分得以防止引入可能破壞規範理論的項目。直到數十年後，物理學家才以BRST替代路徑積分的存在。 在20世紀80年代末，當量子場論得以解決低維流形拓撲結構的問題，BRST量子化變得比在利用以反常抵消解決鬼場的方法更有效。這種修改原始作用量，添加進去一個額外的場（鬼場）並打破規範對稱性的方法，即被稱作「法捷耶夫-波波夫方法」。至於規範不變性和BRST不變性之間的關係，使得哈密頓系統的狀態由粒子的規範量子化選擇。此外，在某些情況下，特別是重力和超引力，BRST必須由更一般的形式，例如以巴塔林-維爾可維斯基代數取代。 (zh) In theoretical physics, the BRST formalism, or BRST quantization (where the BRST refers to the last names of Carlo Becchi, , Raymond Stora and Igor Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier quantum field theory (QFT) frameworks resembled "prescriptions" or "heuristics" more than proofs, especially in non-abelian QFT, where the use of "ghost fields" with superficially bizarre properties is almost unavoidable for technical reasons related to renormalization and anomaly cancellation. (en) Метод квантования Бекки — Руэ́ — Стора́ — Тютина (BRST-квантование) — метод теоретической физики, использующий строгий подход к квантованию теории поля при наличии калибровочной симметрии. Назван по именам (англ. Carlo Becchi), Алена Руэ (Alain Rouet), (фр. Raymond Stora) и Игоря Тютина. В определенных случаях, в частности в теориях гравитации и супергравитации, BRST-квантование должно быть заменено более общим формализмом . (ru) |
| rdfs:label | BRST-Symmetrie (de) BRST quantization (en) BRST 양자화 (ko) Метод квантования Бекки — Руэ — Стора — Тютина (ru) BRST量子化 (zh) |
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