Different canonical formalisms for higher order theories lead to different phase-space structures of the Hamiltonian. Canonical equivalence of these Hamiltonians at the classical level does not assure the same in the quantum domain, due to nonlinearity. It has been proved in the isotropic models, that the “Dirac constraint analysis” (after taking care of divergent terms) and “Modified Horowitz Formalism” lead to identical phase-space structure of the Hamiltonian for the gravitational action with curvature squared terms. Here, we extend the same in anisotropic space-time, viz, Bianchi-I, Bianchi-III and Kantowski–Sachs models too. This is a prologue toward canonical quantization.

中文翻译：

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高阶引力理论各向异性模型的典型等价

高阶理论的不同规范形式导致哈密顿量的不同相空间结构。由于非线性，这些哈密顿量在经典水平上的典型等价并不能保证在量子域中的相同。在各向同性模型中已经证明，“狄拉克约束分析”（在考虑了发散项之后）和“修正霍洛维茨形式主义”导致具有曲率平方项的引力作用的哈密顿量相同的相空间结构。在这里，我们在各向异性时空模型中也进行了同样的扩展，即 Bianchi-I、Bianchi-III 和 Kantowski-Sachs 模型。这是规范量化的序幕。