论文标题
在四维空间中的二阶，双形式不变的标量张量理论
Second-Order, Biconformally Invariant Scalar-Tensor Field Theories in a Four-Dimensional Space
论文作者
论文摘要
在本文中，我将在四维空间中考虑字段理论，该空间具有由度量张量和标量场的组成部分组成的场变量。这些标量调整的字段理论的字段方程将使用拉格朗日标量密度从变分原理中得出，这是磁场变量及其任意但有限顺序的衍生物的伴随。我将考虑场变量的双符号变换，它们是影响度量张量和标量场的共形变换。将开发出必要且充分的条件，以确定何时欧拉 - 拉格朗格张量密度是双形的不变性。该条件将用于构建四维空间中的所有二阶双形不变标量探测场理论。事实证明，这些理论的字段方程可以源自（最多）两个二阶Lagrangians的线性组合，而线性组合中的系数为真实常数。
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.
