Related papers: Localization and diffusion in polymer quantum fiel…
In effective models of loop quantum gravity, the onset of quantum effects is controlled by a so-called polymerisation scale. It is sometimes necessary to make this scale phase space dependent in order to obtain sensible physics. A…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
This is the introductory chapter to the volume. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…
We study the effective dynamics of a polymer quantized scalar field living on an effective polymer quantized homogeneous and isotropic background. We use a presureless dust field as an internal clock, and work with volume variables. Our…
We study the semiclassical dynamics of a polymer quantized scalar field with a cubic potential in cosmology. The cosmological spacetime is chosen to be homogeneous and isotropic, and we work in the polymer quantization scheme where the…
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of…
A phenomenological model of the time evolution of a particle wavepacket is presented that is subject to scattering event with small momentum transfer. It is suited for three dimensions and allows for an additional potential. For a random…
We apply a type of background independent "polymer" quantization to a free scalar field in a flat spacetime. Using semi-classical states, we find an effective wave equation that is both nonlinear and Lorentz invariance violating. We solve…
It is often overlooked that local quantum physics has a built in quantum localization structure which may under certain circumstances disagree with (differential, algebraic) geometric ideas. String theory originated from such a spectacular…
We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of…
We recently studied gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since there are local degrees of freedom one faces the "problem of dynamics". We attack it using the "uniform discretization…
We examine the dependence of quantization on global properties of a classical system. Quantization based on local properties may lead to ambiguities and inconsistency between local and global symmetries of a quantum system. Our quantization…
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational…
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We show that a freely moving particle measured in this way undergoes superdiffusion, while a charged particle moving in a…
Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer…