Related papers: A Path-integral for the Master Constraint of Loop …
We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in…
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In the series of papers, we will introduce a graphical method, developed by Yutsis and Brink, to loop…
Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical…
Recently the Master Constraint Programme for Loop Quantum Gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler -- DeWitt constraint equations in terms of a single Master Equation. While the…
Path integral quantization of quantum gauge general relativity is discussed in this paper. First, we deduce the generating functional of green function with external fields. Based on this generating functional, the propagators of…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
As modified gravity theories, the 4-dimensional metric $f(R)$ theories are cast into connection dynamical formalism with real $su(2)$-connections as configuration variables. This formalism enables us to extend the non-perturbative loop…
This is the fourth paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. We now move on to free field theories with constraints, namely Maxwell theory…
Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of…
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction…
We revise imposition of various constraints in spin foam models of 4-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted…
The authors apply the generalized master equation to analyze time-dependent transport through a finite quantum wire with an embedded subsystem. The parabolic quantum wire and the leads with several subbands are described by a continuous…
We couple to group field theory (GFT) a scalar field that encodes the entanglement between manifold sites. The scalar field provides a relational clock that enables the derivation of the Hamiltonian of the system from the GFT action.…
The quantum-reduced loop-gravity technique has been introduced for dealing with cosmological models. We show that it can be applied rather generically: anytime the spatial metric can be gauge-fixed to a diagonal form. The technique selects…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…
The semiclassical solution of quantum Dirac constraints in generic constrained system is obtained by directly calculating in the one-loop approximation the gauge field path integral with relativistic gauge fixing procedure. The gauge…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz and Zhang, which was based on the direct computation of path…
I argue that the complete partition function of 3D quantum gravity is given by a path integral over gauge-inequivalent manifolds times the Chern-Simons partition function. In a discrete version, it gives a sum over simplicial complexes…