Related papers: Polymer quantization and Symmetries
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…
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 construct the Hamiltonian formulation of the isotropic Universe in a generic metric f(R)-theory in the Jordan frame. We canonically quantize the Universe volume via a polymer formulation, and we adopt the scalar field naturally arising…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
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…
We analyze the effective dynamics of a polymer quantized homogeneous and anisotropic Bianchi-I universe coupled to a polymer quantized scalar field. We use a pressureless dust field as an internal clock, and work with the gravitational…
In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be…
We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies…
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the…
In this paper, we study the statistical mechanics within the polymer quantization framework in the semiclassical regime. We apply a non-canonical transformation to the phase space variables. Then, we use this non-canonical transformation to…
Polarization is one of light's most versatile degrees of freedom for both classical and quantum applications. The ability to measure light's state of polarization and changes therein is thus essential; this is the science of polarimetry. It…
The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum…
In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a…
We present a polymer(loop) quantization of a two dimensional theory of dilatonic gravity known as the CGHS model. We recast the theory as a parametrized free field theory on a flat 2-dimensional spacetime and quantize the resulting phase…
We develop a suitable technical algorithm to implement a separation of the Minisuperspace configurational variables into quasi-classical and purely quantum degrees of freedom, in the framework of a Polymer quantum Mechanics reformulation of…
The role of symmetries in formation of quantum dynamics is discussed. A quantum version of the d'Alambert's principle is proposed to take into account symmetry constrains for quantum case. It is noted that in this approach one can find, in…
In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…
In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to…
Considerable attention has been paid to the study of the quantum geometry of nonrotating black holes within the framework of Loop Quantum Cosmology. This interest has been reinvigorated since the introduction of a novel effective model by…
We present a polymer quantization of the -lambda/r^2 potential on the positive real line and compute numerically the bound state eigenenergies in terms of the dimensionless coupling constant lambda. The singularity at the origin is handled…