论文标题
来自空间协变重力的较高衍生标量调整理论：线性代数分析
Higher derivative scalar-tensor theory from the spatially covariant gravity: a linear algebraic analysis
论文作者
论文摘要
我们使用标量标量字段研究了无幽灵标量调整理论，标量字段的衍生物直至第三阶和riemann张量，直至二次顺序。我们构建两种类型的线性空间。一个是线性独立的一组通常协变标量张量单元，另一个是线性独立的空间协变量单元。我们认为，这两种类型的线性空间在量规固定/恢复过程的意义上是彼此同构的。然后，我们识别空间协变量中的子空间，这些子空间由由外在和内在曲率构建的线性独立的单体跨度跨越，散失功能及其空间衍生物在衍生物总数中达到第四阶。这些子空间中的矢量，即在空间协变的多项式，自动在最多三个自由度中传播。结果，他们在仪表恢复映射的量规下的图像自动是标量张量理论的子空间，只要标量场是及时的，它们就会传播到三个自由度。从空间协方差的重力到标量探测理论空间的映射在投影矩阵中编码，我们也明确地得出了表达式。我们的形式主义和结果对于得出没有鬼魂的普遍协变量标量探望理论可能是有用的。
We investigate the ghostfree scalar-tensor theory with a timelike scalar field, with derivatives of the scalar field up to the third order and with the Riemann tensor up to the quadratic order. We build two types of linear spaces. One is the set of linearly independent generally covariant scalar-tensor monomials, the other is the set of linearly independent spatially covariant gravity monomials. We argue that these two types of linear space are isomorphic to each other in the sense of gauge fixing/recovering procedures. We then identify the subspaces in the spatially covariant gravity, which are spanned by linearly independent monomials built of the extrinsic and intrinsic curvature, the lapse function as well as their spatial derivatives, up to the fourth order in the total number of derivatives. The vectors in these subspaces, i.e., spatially covariant polynomials, automatically propagate at most three degrees of freedom. As a result, their images under the gauge recovering mappings are automatically the subspaces of scalar-tensor theory that propagate up to three degrees of freedom as long as the scalar field is timelike. The mappings from the spaces of spatially covariant gravity to the spaces of scalar-tensor theory are encoded in the projection matrices, of which we also derived the expressions explicitly. Our formalism and results can be useful in deriving the generally covariant higher derivative scalar-tensor theory without ghost(s).
