Related papers: Frozen formalism and canonical quantization in gro…
It is shown that the difficulties in formulating the quantum field theory on discrete spacetime appear already in classical dynamics of one degree of freedom on discrete time. The difference equation of motion which maintains a conserved…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…
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…
One of the hardest problems to tackle in the dynamics of canonical approaches to quantum gravity is that of the Hamiltonian constraint. We investigate said problem in the context of formal geometric quantization. We study the implications…
We perform canonical quantization of General Relativity, as an effective quantum field theory below the Planck scale, within the BRST-invariant framework. We show that the promotion of constraints to dynamical equations of motion for…
Fermions are coupled to the Einstein-Cartan system in the canonical formulation, including the cosmological, the Barbero-Immirzi, and the non-minimal coupling constants. The resulting ten first-class constraints generate gauge…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
A classical field theory is proposed for the electric current and the electromagnetic field interpolating between microscopic and macroscopic domains. It represents a generalization of the density functional for the dynamics of the current…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
A starting point for the present work was the statement recently discussed in the literature that two Hamiltonian formulations for the theory of gravity, the one proposed by Dirac and the other by Arnowitt - Deser - Misner, may not be…
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…
Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the…
We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an…
The problem of defining and constructing representations of the Canonical Commutation Relations can be systematically approached via the technique of {\it algebraic quantization}. In particular, when the phase space of the system is linear…
On the basis of dynamic quantization method we build in this paper a new mathematically correct quantization scheme of gravity. In the frame of this scheme we develop a canonical formalism in tetrad-connection variables in 4-D theory of…
Recent results based on renormalization group approaches to Quantum Gravity suggest that the Newton's and cosmological constants should be treated as dynamical variables whose evolution depend on the characteristic energy scale of the…
We present an anomaly-free Dirac constraint quantization of the string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional spacetime. We show that the quantum theory has the same degrees of freedom as the classical theory;…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…