Gauge-invariant quadratic approximation of quasi-local mass and its relation with Hamiltonian for gravitational field

Hamiltonian Formulation of Bianchi Cosmological Models in Quadratic Theories of Gravity

We use Boulware's Hamiltonian formalism of quadratic gravity theories in order to analyze the classical behaviour of Bianchi cosmological models for a Lagrangian density containing quadratic terms in the curvature. For this purpose we define a canonical transformation which leads to a clear distinction between two main variants of the quadratic theory, namely the R-squared or conformal Lagrangian densities. In this paper we restrict the study to the first variant. For Bianchi type I and IX models we give the explicit forms of the super-Hamiltonian constraint, of the ADM Hamiltonian density and…

二次引力的哈密顿运动方程

Hamiltonian equations of motion of quadratic gravity

本文研究了二次引力的哈密顿运动方程，通过符号计算工具Cadabra进行明确计算，并探讨了线性方程与协变场方程的比较，发现迹零条件对线性哈密顿形式的有效性至关重要。

Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes

We obtain the quadratic-in-spin terms of the conservative Hamiltonian describing the interactions of a binary of spinning bodies in General Relativity through $\mathcal{O}(G^2)$ and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory to consider non-minimal coupling of the spinning objects to gravity. At the order that we consider, we establish the validity of the formula proposed in \cite{Bern:2020buy} that relates the impulse and spin kick in a scattering event to the eikonal phase.

Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic Hamiltonian. The growth rate does not depend on the initial state and is equal to the sum of certain Lyapunov exponents of the corresponding classical dynamics. This paper generalizes the findings of [Bianchi et al., JHEP 2018, 25 (2018)], which proves the same result in the special case of Gaussian initial states. Our proof is based on a recent generalization of the strong subadditivity of the von Neumann e…

Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin

We derive a Hamiltonian for an extended spinning test body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This requires a careful analysis of how changes of the spin supplementary condition are related to shifts of the body's representative worldline and transformations of the body's multipole moments, and we employ bitensor calculus for a precise framing of this analysis. We apply the result to the case of the Kerr spacetime and thereby compute an explicit canonical Hamil…

后牛顿框架下NNNLO阶引力自旋平方哈密顿量

Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework

本文采用有效场论图解方法，计算了旋转致密天体双星系统在NNNLO阶的自旋平方相互作用哈密顿量，推导了规范不变的结合能与散射角，扩展了自旋-轨道相互作用的研究。