Related papers: The Extended Loop Representation of Quantum Gravit…
We extend the thermodynamic derivation of gravity in the Jacobson framework by generalizing the Clausius relation through a nontrivial entropy functional. We show that entropy deformations appear as modifications of the effective…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
The structure of extended loop wave function is investigated in terms of the operator formalism. It is found that the extended loop wave function is characterized by the family number and classified by the partition of the family number. It…
Based on a family of indefinite unitary representations of the diffeomorphism group of an oriented smooth $4$-manifold, a manifestly covariant $4$ dimensional and non-perturbative algebraic quantum field theory formulation of gravity is…
Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be…
A nonperturbative approach to quantum gravity that has generated much discussion is the attempt to construct a ``loop representation." Despite it's success in linear quantum theories and a part of 2+1 quantum gravity, it has recently been…
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…
I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a…
Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field…
The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie…
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…
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to…
In [1] we initiated an approach towards quantizing the Hamiltonian constraint in Loop Quantum Gravity (LQG) by requiring that it generates an anomaly-free representation of constraint algebra off-shell. We investigated this issue in the…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We…
It has been pointed out that the holonomy of generic extended loops is not gauge covariant. We show how to define a family of extended loops for which previous criticism does not apply. We also give sufficient conditions that extended loops…