Loop quantum black hole extensions within the improved dynamics

Spherically symmetric loop quantum gravity: analysis of improved dynamics

We study the "improved dynamics" for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou {\em et al.} in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space-times. In this dynamics the polymerization parameter is a well motivated function of the dynamical variables, reflecting the fact that the quantum of area depends on them. Contrary to the homogeneous case, its implementation does not trigger undesirable physical properties. We identify semiclassical physical states in the quantum theory and der…

Loop quantization of spherically symmetric midisuperspaces and loop quantum geometry of the maximally extended Schwarzschild spacetime

We elaborate on the Ashtekar's formalism for spherically symmetric midisuperspaces and, for loop quantization, propound a new quantization scheme which yields a graph-preserving Hamiltonian constraint operator and by which one can impose the fundamental discreteness of loop quantum gravity a la the strategy of "improved" dynamics in loop quantum cosmology (LQC). Remarkable consequences are inferred at the heuristic level of effective dynamics: first, consistency of the constraint algebra regarding the Hamiltonian and diffeomorphism constraints fixes the improved quantization scheme to be of th…

Improved ($\barμ$-Scheme) Effective Dynamics of Full Loop Quantum Gravity

We propose a new derivation from the full Loop Quantum Gravity (LQG) to the Loop Quantum Cosmology (LQC) improved $\barμ$-scheme effective dynamics, based on the reduced phase space formulation of LQG and a proposal of effective Hamiltonian/action in the full LQG. A key step of our program is an improved regularization of the full LQG Hamiltonian on a cubic lattice. The improved Hamiltonian uses a set of "dressed holonomies" $h_Δ(\mathfrak{s})$ which not only depend on the connection $A$ but also depend on the length of the curve $\mathfrak{s}$. With the improved Hamiltonian, we propose a quan…

Automorphisms in Loop Quantum Gravity

We investigate a certain distributional extension of the group of spatial diffeomorphisms in Loop Quantum Gravity. This extension, which is given by the automorphisms Aut(P) of the path groupoid P, was proposed by Velhinho and is inspired by category theory. This group is much larger than the group of piecewise analytic diffeomorphisms. In particular, we will show that graphs with the same combinatorics but different generalized knotting classes can be mapped into each other. We describe the automorphism-invariant Hilbert space and comment on how a combinatorial formulation of LQG might arise.

有效圈量子引力中冲击波动力学的非唯一性

Non-uniqueness of the shockwave dynamics in effective loop quantum gravity

本文证明有效圈量子引力中冲击波时空延拓不唯一，黑洞寿命等关键特征取决于运动方程积分形式的选择。

圈量子宇宙学中的幺正演化与宇宙加速

Unitary evolution and cosmic acceleration in Loop Quantum Cosmology

本研究在圈量子宇宙学中探讨任意权重下模型的幺正演化，发现非正权重时幺正性成立，正值时需自伴扩展，并在传播子中实现以涵盖观测结果。

Extension of loop quantum gravity to $f(R)$ theories

The 4-dimensional metric $f(\R)$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\R)$ theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the non-perturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity.

Quantum Nature of the Big Bang: Improved dynamics

An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as `emergent time', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint i…

Extended Loops: A New Arena for Nonperturbative Quantum Gravity

We propose a new representation for gauge theories and quantum gravity. It can be viewed as a generalization of the loop representation. We make use of a recently introduced extension of the group of loops into a Lie Group. This extension allows the use of functional methods to solve the constraint equations. It puts in a precise framework the regularization problems of the loop representation. It has practical advantages in the search for quantum states. We present new solutions to the Wheeler-DeWitt equation that reinforce the conjecture that the Jones Polynomial is a state of nonperturbativ…

Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity

The successful background-independent quantization of Loop Quantum Gravity relies on the key observation that classical General Relativity can be cast into the connection-dynamical formalism with the structure group of SU(2). Due to this particular formalism, Loop Quantum Gravity was generally considered as a quantization scheme that applies only to General Relativity. However, we will show that the nonperturbative quantization procedure of Loop Quantum Gravity can be extended to a rather general class of metric theories of gravity, which have received increased attention recently due to motiv…

利用银心恒星对圈量子引力中施瓦西时空量子扩展的观测检验

Observational tests of quantum extension of Schwarzschild spacetime in loop quantum gravity with stars in the galactic center

本研究利用银心17颗绕Sgr A*运行恒星的观测数据，通过测地线演化转化与MCMC模拟检验圈量子引力的施瓦西时空量子扩展模型，未发现相关显著证据，并由S2星给出LQG参数95%置信度的最强上限约束。

Loop Quantum Gravity on Dynamical Lattice and Improved Cosmological Effective Dynamics with Inflaton

In the path integral formulation of the reduced phase space Loop Quantum Gravity (LQG), we propose a new approach to allow the spatial cubic lattice (graph) to change dynamically in the physical time evolution. The equations of motion of the path integral derive the effective dynamics of cosmology from the full LQG, when we focus on solutions with homogeneous and isotropic symmetry. The resulting cosmological effective dynamics with the dynamical lattice improves the effective dynamics obtained earlier from the path integral with fixed spatial lattice: The improved effective dynamics recovers …

Issues Concerning Loop Corrections to the Primordial Power Spectra

We expound ten principles in an attempt to clarify the debate over infrared loop corrections to the primordial scalar and tensor power spectra from inflation. Among other things we note that existing proposals for nonlinear extensions of the scalar fluctuation field $ζ$ introduce new ultraviolet divergences which no one understands how to renormalize. Loop corrections and higher correlators of these putative observables would also be enhanced by inverse powers of the slow roll parameter $ε$. We propose an extension which should be better behaved.

One-loop stress-tensor renormalization in curved background: the relation between $ζ$-function and point-splitting approaches, and an improved point-splitting procedure

We conclude the rigorous analysis of a previous paper concerning the relation between the (Euclidean) point-splitting approach and the local $ζ$-function procedure to renormalize physical quantities at one-loop in (Euclidean) QFT in curved spacetime. The stress tensor is now considered in general $D$-dimensional closed manifolds for positive scalar operators $-Δ+ V(x)$. Results obtained in previous works (in the case D=4 and $V(x) =ξR(x) + m^2$) are rigorously proven and generalized. It is also proven that, in static Euclidean manifolds, the method is compatible with Lorentzian-time analytic c…