Related papers: Conserved quantities in isotropic loop quantum cos…
In the framework of loop quantum cosmology anomaly free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of the construction in (non-symmetric) loop…
We derive the effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) in the asymptotic limit where the restoring forces tend to infinity. In contrast to…
In contrast to previous work in the field, we construct the Loop Quantum Cosmology (LQC) of the flat isotropic model with a massless scalar field in the absence of higher order curvature corrections to the gravitational part of the…
The isotropic harmonic oscillator in dimension 3 separates in several different coordinate systems. Separating in a particular coordinate system defines a system of three commuting operators, one of which is the Hamiltonian. We show that…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
It is shown that the difficulties in formulating the quantum field theory on discrete spacetime appear already in classical dynamics of one degree of freedom on discrete time. The difference equation of motion which maintains a conserved…
In this letter we investigate a class of Hamiltonians which, in addition to the usual center-of-mass (CM) momentum conservation, also have center-of-mass position conservation. We find that regardless of the particle statistics, the energy…
In this paper the Hamiltonian of quantum electrodynamics with spatial cutoffs is investigated. We define a scaled total Hamiltonian and consider its asymptotic behavior. In the main theorem, it is shown that the scaled total Hamiltonian…
It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric can be damped by quantum fluctuations coming from perturbative quantum gravity in one-loop approximation. Also, a formal argument, not limited…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity,…
Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This…
A temporally discrete Schroedinger time evolution equation is proposed for isotropic quantum cosmology coupled to a massless scalar source. The approach employs dynamically determined intrinsic time and produces the correct semiclassical…
The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero-Immirzi parameter \gamma in controlling space-time discreteness. In this way,…
Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large…
We show that the equation of quasigeostrophic (QG) potential vorticity conservation in geophysical fluid dynamics follows from Hamilton's principle for stationary variations of an action for geodesic motion in the f-plane case or its…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
In these notes we address the canonical quantization of the cosmological models which appear as solutions of the low energy effective action of closed bosonic string theory (dilaton models). The analysis is restricted to the quantization of…
The evolutions of linear structures in a spatially homogeneous and isotropic world model are characterized by some conserved quantities: the amplitude of gravitational wave is conserved in the super-horizon scale, the perturbed three-space…
In general relativity, the notion of mass and other conserved quantities at spatial infinity can be defined in a natural way via the Hamiltonian framework: Each conserved quantity is associated with an asymptotic symmetry and the value of…