高阶引力理论的等价和不等价正则结构
Equivalent and inequivalent canonical structures of higher order theories of gravity
摘要：
高阶引力理论的正则公式只能通过附加的自由度来实现，而附加的自由度是外曲率张量。因此，为了使柯西数据与边界数据相匹配，除了三空间度量之外的项也必须在边界处固定。在Ostrogradski、Dirac和Horowitz的形式中，外曲率张量在边界处保持不变，而修改后的Horowitz形式则固定Ricci标量。它已被视为理所当然的哈密顿结构对应于所有的形式主义与不同的端点数据是相同的或正则等价的。在目前的研究中，我们表明，这确实是真的，但只有一类高阶理论。然而，对于更一般的高阶理论，例如在曲率平方项存在下的双曲耦合Gauss-Bonnet引力，用修正的Horowitz形式得到的哈密顿量与其它的哈密顿量不同，并且在正则变换下不相关。此外，它也被证明，虽然所有的形式主义产生可行的量子描述，动力学是不同的，而不是规范相关的修改霍洛维茨的形式主义。因此，不可能选择正确的形式主义，这将导致哈密顿量的退化。
英文摘要：
Canonical formulation of higher order theory of gravity can only be accomplished associating additional degrees of freedom, which are extrinsic curvature tensor. Consequently, to match Cauchy data with the boundary data, terms in addition to the three-space metric, must also be fixed at the boundary. While, in all the three, viz. Ostrogradski's, Dirac's and Horowitz' formalisms, extrinsic curvature tensor is kept fixed at the boundary, a modified Horowitz' formalism fixes Ricci scalar, instead. It has been taken as granted that the Hamiltonian structure corresponding to all the formalisms with different end-point data are either the same or are canonically equivalent. In the present study, we show that indeed it is true, but only for a class of higher order theory. However, for more general higher order theories, e.g. dilatonic coupled Gauss-Bonnet gravity in the presence of curvature squared term, the Hamiltonian obtained following modified Horowitz' formalism is found to be different from the others, and is not related under canonical transformation. Further, it has also been demonstrated that although all the formalisms produce viable quantum description, the dynamics is different and not canonically related to modified Horowitz' formalism. Therefore it is not possible to choose the correct formalism which leads to degeneracy in Hamiltonian.
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