A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some cases. A starting point for the systematic study of the solutions of Einstein gravity is suggested.
We present the Hamiltonian formulation of the Ghost Free Mimetic Massive Gravity theory. The linearized theory is studied and the Hamiltonian equations of motion are analyzed. Poisson brackets are computed and closure is proved. To prove that this theory is ghost-free, the number of degrees of freedom is analyzed showing that we have only five degrees of freedom.
As in the case of Lanczos-Lovelock gravity, the main advantage of F(T) gravity is said to be that it leads to second order field equations, while F(R) gravity theory leads to fourth order equations. We show that it is rather a disadvantage, since it leads to the unresolved issue of `Branched Hamiltonian'. The problem is bypassed in F(R,T) gravity theory.
We construct a Hamiltonian for the nonlocal F(R) theory in the present work. By this construction, we demonstrate the nature of the ghost degrees of freedom. Finally, we find conditions that give rise to ghost-free theories
We perform the Hamiltonian analysis of unimodular gravity in terms of the connection representation. The unimodular condition is imposed straightforwardly into the action with a Lagrange multiplier. After classifying constraints into first class and second class, the canonical quantization is carried out. We consider the difference of the corresponding physical states between unimodular gravity and general relativity.
A crucial property of Weyl gravity is its conformal invariance. It is shown how this gauge symmetry is exactly reflected by the two constraints in the Hamiltonian framework. Since the spatial 3-metric is one of the configuration variables, the phase space of Weyl gravity can be extended to include internal gauge freedom by triad formalism. Moreover, by canonical transformations, we obtain two new Hamiltonian formulations of Weyl gravity with an SU(2) connection as one of its configuration variables. The connection-dynamical formalisms lay the foundation to quantize Weyl gravity nonperturbative…
Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein Hilbert action. Here we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Ricci tensor and Ricci scalar. We also show how to count the degree of freedom using Hamiltonian formalism in this model.
The Hamiltonian formalism of Einstein--Cartan (EC) gravity is a starting point for canonical quantum gravity. The existing formalisms are at most Lorentz covariant, or diffeomorphism covariant. Here we analyze the Hamiltonian EC gravity in a 5d covariant way, with the gauge group being the de Sitter (dS) group, which unifies the Lorentz transformations and translation in an elegant manner, and also coincides with the acceleration of the universe. We reformulate the EC equations into a dS-covariant form, then find out the dS-covariant constraints of the phase space, and make all the constraint …
We review different approaches to the Hamiltonian analysis of teleparallel theories of gravity. In particular the Hamiltonian analysis for $f(\mathbb{T})$ theories led to disputed results in the literature. The aim of this review is to relate the different notations and assumptions in the different approaches in a comprehensive way, so that they can be compared more easily. To do this we present the primary constraints of the $f({\mathbb{T}_{\textrm{NGR}}})$ gravity class of theories for the first time. The particular cases studied in the literature, $f(\mathbb{T})$ gravity and new general rel…
The existence of an extra degree of freedom (d.o.f.) in $f(T)$ gravity has been recently proved by means of the Dirac formalism for constrained Hamiltonian systems. We will show a toy model displaying the essential feature of $f(T)$ gravity, which is the pseudoinvariance of T under a local symmetry, to understand the nature of the extra d.o.f.
Several alternative formulations of the first order approach to unimodular gravity are presented. There is always a particular one such that it is {\em classically} equivalent to the second order formulation; this we call {\em educated}. It is often at variance with the {\em naive} approach, in which the lagrangian is taken as given exactly by the same expression as in the second order formulation; only the number and character of the independent variables changes. Namely, typically some of the momenta are now considered as coordinates. The ensuing Hamiltonians are thereby discussed and their …
We provide a constrained Hamiltonian analysis of a non relativistic Schrodinger field in 2+1 dimensions , coupled with Chern - Simons gravity. The coupling is achieved by the recently advanced Galilean gauge theory \cite{BMM1},\cite{ BMM2}, \cite{BM4}. The calculations are repeated with a truncated model to show that deviation from Galilean gauge theory makes the theory untenable. The issue of nonrelativistic spatial diffeomorphism is discussed in this context.
Although the physical Hamiltonian operator can be constructed in the deparameterized model of loop quantum gravity coupled to a scalar field, its property is still unknown. This open issue is attacked in this paper by considering an operator $\hat{H}_v$ representing the square of the physical Hamiltonian operator acting nontrivially on two-valent spin networks. The Hilbert space $\mathcal{H}_v$ preserved by the graphing changing operator $\hat{H}_v$ is consist of spin networks with a single two-valent non-degenerate vertex. The matrix element of $\hat{H}_v$ are explicitly worked out in a suita…
We introduce a new regularization scheme for Quantum Cosmology in Loop Quantum Gravity (LQG) using the tools of Quantum Reduced Loop Gravity (QRLG). It is obtained considering density matrices for superposition of graphs based on statistical countings of microstates compatible with macroscopic configurations. We call this procedure statistical regularization scheme. In particular, we show how the $μ_0$ and $\barμ$ schemes introduced in Loop Quantum Cosmology (LQC) emerge with specific choices of density matrices. Within this new scheme we compute effective Hamiltonians suitable to describe qua…
Introducing a new method, we demonstrate how the action of reduced operators can be derived without resorting to a recoupling theory and how they exactly reproduce the results obtained in the standard approach of Quantum Reduced Loop Gravity (QRLG). This is particularly relevant while dealing with volume operator when dealing with the coupling of matter fields to gravity. Apart from reinforcing the close link between QRLG and loop quantum cosmology (LQC), this procedure also sheds new light on the issue of how to extract the continuum limit, without resorting to the large-$j$ expansion, thereb…
The Hamiltonian formulation of the lowest-order projectable Horava gravity, namely the so-called $λ$-$R$ gravity, is studied. Since a preferred foliation has been chosen in projectable Horava gravity, there is no local Hamiltonian constraint in the theory. In contrast to general relativity, the constraint algebra of $λ$-$R$ gravity forms a Lie algebra. By canonical transformations, we further obtain the connection-dynamical formalism of the $λ$-R gravity theories with real $su(2)$-connections as configuration variables. This formalism enables us to extend the scheme of non-perturbative loop qu…
Covariant Hamiltonian formulation of $F(R)$ gravity is used to find variation of surface Hamiltonian which leads to formulation of temperature and entropy of a horizon. These thermodynamic quantities are then used to establish an analogy between Einstein equation and Clausius equation. The obtained results are compared to those from classical General Relativity.
Hamiltonian dynamics in extended phase space for gravity and its consistency with Lagrangian formalism: a generalized spherically symmetric model as an example
Quantum Geometry Effects in Quantum Field Theory: Hamiltonian constraint Generates Gravity-Matter Entanglement
School of Physics and Astronomy, Key Laboratory of Multiscale Spin Physics, Ministry of Education, Beijing Normal University（北京师范大学物理与天文学院，教育部多尺度自旋物理重点实验室）
