Related papers: Quantization Viewed as Galois Extension
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
We present a new interpretation of the terms superposition, entanglement, and measurement that appear in quantum mechanics. We hypothesize that the structure of the wave function for a quantum system at the sub-Planck scale has a…
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…
We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries…
In quantum field theory, elemental particles are assumed to be point particles. As a result, the loop integrals are divergent in many cases. Regularization and renormalization are necessary in order to get the physical finite results from…
Coupling any interacting quantum mechanical system to gravity in one (time) dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantised, even though the gravity sector is free of any quantum…
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…
We develop a formalism to calculate the response of a model gravitational wave detector to a quantized gravitational field. Coupling a detector to a quantum field induces stochastic fluctuations ("noise") in the length of the detector arm.…
The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It…
We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer…
A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their…
Circuit quantization links a physical circuit to its corresponding quantum Hamiltonian. The standard quantization procedure generally assumes any external magnetic flux to be static. Time dependence naturally arises, however, when flux is…
I construct lowest-energy representations of non-centrally extended algebras of Noether symmetries, including diffeomorphisms and reparametrizations of the observer's trajectory. This may be viewed as a new scheme for quantization. First…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
A generalization of the recently formulated nonlinear quantization of a parameterized theory is presented in the context of quantum gravity. The parametric quantization of a Friedmann universe with a massless scalar field is then considered…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…