Related papers: Background independent quantizations: the scalar f…
We consider the world-line quantisation of a system invariant under the symmetries of reciprocal relativity. Imposition of the first class constraint, the generator of local time reparametrisations, on physical states enforces…
Polymer Quantization (PQ) is a background independent quantization scheme that is deployed in Loop Quantum Gravity. This framework leads to a new short-distance (discretized) structure characterized by a fundamental length. In this paper we…
We achieve a group theoretical quantization of the flat Friedmann-Robertson-Walker model coupled to a massless scalar field adopting the improved dynamics of loop quantum cosmology. Deparemeterizing the system using the scalar field as…
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied…
We study free scalar field theory on flat spacetime using a background independent (polymer) quantization procedure. Specifically we compute the propagator using a method that takes the energy spectrum and position matrix elements of the…
A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on…
The inverse scale factor, which in classical cosmological models diverges at the singularity, is quantized in isotropic models of loop quantum cosmology by using techniques which have been developed in quantum geometry for a quantization of…
A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum…
The linearly polarized Gowdy $T^3$ model with a massless scalar field with the same symmetries as the metric is quantized by applying a hybrid approach. The homogeneous geometry degrees of freedom are loop quantized, fact which leads to the…
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation,…
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…
Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity.…
In this work, we study the quantization of Carrollian conformal scalar theories, including two-dimensional(2D) magnetic scalar and three-dimensional(3D) electric and magnetic scalars. We discuss two different quantization schemes, depending…
We quantize to completion an inflationary universe with small inhomogeneities in the framework of loop quantum cosmology. The homogeneous setting consists of a massive scalar field propagating in a closed, homogeneous scenario. We provide a…
We discuss the algebraic quantization of a real, massive scalar field in the Poincar\'e patch of the (d+1)-dimensional anti-de Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is…
A covariant scalar representation of $iosp(d,2/2)$ is constructed and analysed in comparison with existing methods for the quantization of the scalar relativistic particle. It is found that, with appropriately defined wavefunctions, this…
We apply a singularity resolution technique utilized in loop quantum gravity to the polymer representation of quantum mechanics on R with the singular -1/|x| potential. On an equispaced lattice, the resulting eigenvalue problem is identical…
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…
Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the…
The terms in the quantum scattering in scalar field theory models is parameterized by the invariants $\prod s_{ij}^{n_{ij}}$. The $s_{ij}$ are kinematic two-particle invariants, and the $n_{ij}$ are integers. The coefficients of these terms…