相关论文: Bohr-Sommerfeld Quantization of Space

A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space…

We analyze the spectrum of the 3-site Bose-Hubbard model with periodic boundary conditions using a semiclassical method. The Bohr-Sommerfeld quantization is applied to an effective classical Hamiltonian which we derive using resonance…

We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a…

Interwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret…

In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a…

It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…

We consider a spherical symmetric black hole in the Schwarzschild metric and apply Bohr-Sommerfeld quantization to determine the energy levels. The canonical partition function is then computed and we show that the entropy coincides with…

Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…

The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis,…

This paper extends the Bohr-Sommerfeld quantization of the spherical pendulum to a full quantum theory. This the first application of geometric quantization to a classical system with monodromy.

The Newtonian dynamics of particles in brane gravity is investigated. Due to the coupling of the particles' energy-momentum tensor to the tension of the brane, the particle is semi-confined and oscillates along the extra dimension. We…

We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…

A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…

A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of…

Following Bekenstein's suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the…

We consider the quantization of the midi-superspace associated with a class of spacetimes with toroidal isometries, but without the compact spatial hypersurfaces of the well-known Gowdy models. By a symmetry reduction, the phase space for…

We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its matrix elements, it is possible for the first time to treat…

Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…

A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…

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…