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词汇 covariant-derivative
语种 英语、汉语、英汉翻译、汉英翻译
释义 BETA

covariant derivative

collocation in English

meanings of derivative


These words are often used together. Click on the links below to explore the meanings.
derivative
noun[ C ]
uk /dɪˈrɪv.ə.tɪv/ us /dɪˈrɪv.ə.t̬ɪv/
a form of something made or developed from ...
See more at derivative


Examples of covariant derivative


covariant derivative
Connections (gauge connection) define this principal bundle, yielding a covariantderivative in each associated vector bundle.
From
Wikipedia

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The operator can be extended to operate on tensors as the divergence of the covariantderivative.
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Even to formulate such equations requires a fresh notion, the covariantderivative.
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This regulator is gauge invariant due to the auxiliary particles being minimally coupled to the photon field through the gauge covariantderivative.
From
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The covariantderivative of a tensor field is presented as an extension of the same concept.
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Wikipedia

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In words: the covariantderivative is the usual derivative along the coordinates with correction terms which tell how the coordinates change.
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In addition to its interaction with other objects via the covariantderivative, the gauge field typically contributes energy in the form of a self-energy term.
From
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The connection associated with this covariantderivative is completely determined by the tetrad.
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In curved space-time, we must take the covariantderivative.
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The equivalence of the more traditional general relativistic formulation using the covariant derivative with the differential form formulation can be seen as follows.
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This is the tactic taken by the covariantderivative approach to connections: good behavior is equated with covariance.
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The covariantderivative can in turn be recovered from parallel transport.
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The equivalence principle is not assumed, but instead follows from the fact that the gauge covariantderivative is minimally coupled.
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Wikipedia

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The covariantderivative is convenient however because it commutes with raising and lowering indices.
From
Wikipedia

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The covariantderivative of a tensor field along a vector field v is again a tensor field of the same type.
From
Wikipedia

This example is from Wikipedia and may be reused under a CC BY-SA license.
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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更新时间:2025/7/19 8:39:30