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arXiv 2210.04837gr-qc
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四维空间中的二阶双共形不变标量张量场论

Second-Order, Biconformally Invariant Scalar-Tensor Field Theories in a Four-Dimensional Space

Gregory W. Horndeski

摘要:

在本文中,我将考虑四维空间中的场论,它的场变量由度规张量和标量场的分量组成。这些标量-张量场论的场方程可以从一个使用拉格朗日标量密度的变分原理导出,拉格朗日标量密度是场变量及其任意但有限阶导数的伴随物。我将考虑场变量的双共形变换,这是既影响度规张量又影响标量场的共形变换。一个必要和充分条件将被开发,以确定何时欧拉-拉格朗日张量密度是双共形不变的。这个条件将被用来构造四维空间中所有的二阶双共形不变标量张量场论。事实证明,这些理论的场方程可以从(最多)两个二阶拉格朗日量的线性组合中导出,线性组合中的系数是实常数。

英文摘要:

In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be derivable from a variational principle using a Lagrange scalar density which is a concomitant of the field variables and their derivatives of arbitrary, but finite, order. I shall consider biconformal transformations of the field variables, which are conformal transformations which affect both the metric tensor and scalar field. A necessary and sufficient condition will be developed to determine when the Euler-Lagrange tensor densities are biconformally invariant. This condition will be employed to construct all of the second-order biconformally invariant scalar-tensor field theories in a space of four-dimensions. It turns out that the field equations of these theories can be derived from a linear combination of (at most) two second-order Lagrangians, with the coefficients in that linear combination being real constants.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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