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A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
We construct a counter example showing, for the quadratic quantization, the identity $(\Gamma(T))^*= \Gamma(T^*)$ is not necessarily true. We characterize all operators on the one-particle algebra whose quadratic quantization are…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
Recently, Babenko and Lempitsky introduced Additive Quantization (AQ), a generalization of Product Quantization (PQ) where a non-independent set of codebooks is used to compress vectors into small binary codes. Unfortunately, under this…
We introduce an analogue of the $q$-Schur algebra associated to Coxeter systems of type $\hat A_{n-1}$. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an…
We construct phase-space structure of a typical higher-order theory of gravity, in the background of anisotropic Bianchi-1 mini-superspace, following `Modified Horowitz Formalism' as well as applying `Dirac Algorithm' (after taking care of…
The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that…
Particle localization within quantum field theory is revisited. Canonical quantization of a free scalar field theory is performed in a manifestly Lorentz covariant way with respect to an arbitrary 3-surface $\Sigma$, which is the…
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 general relativity in metric variables using ``precanonical'' quantization based on the De Donder-Weyl covariant Hamiltonian formulation is outlined. Elements of classical geometry needed to formulate the (Dirac-like) wave…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…
For a 1+1 dimensional theory of gravity with torsion different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity…
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 show that all important features of 2d gravity coupled to $c<1$ matter can be easily understood from the canonical quantization approach a la Dirac. Furthermore, we construct a canonical transformation which maps the theory into a…
Quantum Focusing is a powerful conjecture, which plays a key role in the current proofs of many well-known quantum gravity theorems, including various consistency conditions, and causality constraints in AdS/CFT. I conjecture a (weaker)…
The recently introduced manifestly covariant canonical quantization scheme is applied to gravity. New diffeomorphism anomalies generating a multi-dimensional generalization of the Virasoro algebra arise. This does not contradict theorems…
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…