Palatini variation (original) (raw)
팔라티니 변분(Palatini變分, 영어: Palatini variation)은 아인슈타인-힐베르트 작용(및 추가 물질 작용)을 리만 계량 또는 필바인의 2차 도함수에 대한 범함수 대신, 필바인과 스핀 접속의 1차 도함수에 대한 범함수로 여겨 변분법을 가하는 것을 말한다. 이 경우, 필바인은 일종의 보조장을 이루며, 페르미온 물질이 존재할 경우 일반적으로 스핀 접속은 0이 아닌 비틀림 텐서를 갖는다.
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| dbo:abstract | In general relativity and gravitation the Palatini variation is nowadays thought of as a variation of a Lagrangian with respect to the connection. In fact, as is well known, the Einstein–Hilbert action for general relativity was first formulated purely in terms of the spacetime metric . In the Palatini variational method one takes as independent field variables not only the ten components but also the forty components of the affine connection , assuming, a priori, no dependence of the from the and their derivatives. The reason the Palatini variation is considered important is that it means that the use of the Christoffel connection in general relativity does not have to be added as a separate assumption; the information is already in the Lagrangian. For theories of gravitation which have more complex Lagrangians than the Einstein–Hilbert Lagrangian of general relativity, the Palatini variation sometimes gives more complex connections and sometimes tensorial equations. Attilio Palatini (1889–1949) was an Italian mathematician who received his doctorate from the University of Padova, where he studied under Levi-Civita and Ricci-Curbastro. The history of the subject, and Palatini's connection with it, are not straightforward (see references). In fact, it seems that what the textbooks now call "" was actually invented in 1925 by Einstein, and as the years passed, people tended to mix up the Palatini identity and the Palatini formalism. (en) 팔라티니 변분(Palatini變分, 영어: Palatini variation)은 아인슈타인-힐베르트 작용(및 추가 물질 작용)을 리만 계량 또는 필바인의 2차 도함수에 대한 범함수 대신, 필바인과 스핀 접속의 1차 도함수에 대한 범함수로 여겨 변분법을 가하는 것을 말한다. 이 경우, 필바인은 일종의 보조장을 이루며, 페르미온 물질이 존재할 경우 일반적으로 스핀 접속은 0이 아닌 비틀림 텐서를 갖는다. (ko) |
| dbo:wikiPageExternalLink | https://aip.scitation.org/doi/10.1063/1.523699 https://link.springer.com/article/10.1007/BF00756060 https://link.springer.com/article/10.1007/BF03014670 |
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| rdfs:comment | 팔라티니 변분(Palatini變分, 영어: Palatini variation)은 아인슈타인-힐베르트 작용(및 추가 물질 작용)을 리만 계량 또는 필바인의 2차 도함수에 대한 범함수 대신, 필바인과 스핀 접속의 1차 도함수에 대한 범함수로 여겨 변분법을 가하는 것을 말한다. 이 경우, 필바인은 일종의 보조장을 이루며, 페르미온 물질이 존재할 경우 일반적으로 스핀 접속은 0이 아닌 비틀림 텐서를 갖는다. (ko) In general relativity and gravitation the Palatini variation is nowadays thought of as a variation of a Lagrangian with respect to the connection. In fact, as is well known, the Einstein–Hilbert action for general relativity was first formulated purely in terms of the spacetime metric . In the Palatini variational method one takes as independent field variables not only the ten components but also the forty components of the affine connection , assuming, a priori, no dependence of the from the and their derivatives. (en) |
| rdfs:label | 팔라티니 변분 (ko) Palatini variation (en) |
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