Related papers: Uniqueness of minimal loop quantum cosmology dynam…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We show that the quantum linear harmonic oscillator can be obtained in the large $N$ limit of a classical deterministic system with SU(1,1) dynamical symmetry. This is done in analogy with recent work by G.'t Hooft who investigated a…
In this paper we study the effect of a torus topology on Loop Quantum Cosmology. We first derive the Teichmueller space parametrizing all possible tori using Thurston's theorem and construct a Hamiltonian describing the dynamics of these…
A description of the canonical formulation of lineal gravity minimally coupled to N point particles in a circular topology is given. The Hamiltonian is found to be equal to the time-rate of change of the extrinsic curvature multiplied by…
Introducing a new method, we demonstrate how the action of reduced operators can be derived without resorting to a recoupling theory and how they exactly reproduce the results obtained in the standard approach of Quantum Reduced Loop…
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
Excitations of small one-dimensional matter-wave solitons are considered within a framework of the attractive Bose-Hubbard model. The initial eigenstates of the system are found by exact diagonalization of the Bose-Hubbard Hamiltonian. We…
Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian,…
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…
One of the hardest problems to tackle in the dynamics of canonical approaches to quantum gravity is that of the Hamiltonian constraint. We investigate said problem in the context of formal geometric quantization. We study the implications…
Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
The spatially flat and isotropic cosmological model of Brans-Dicke theory with coupling parameter $\omega\neq-3/2$ is quantized by the approach of loop quantum cosmology. An interesting feature of this model is that, although the…
The holomorphic Coulomb gas formalism is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of QFT. We begin with a careful examination…
The version of the cosmological perturbation theory based on exact resolution of energy constraint is developed in accordance with the diffeomorphisms of general relativity in the Dirac Hamiltonian approach. Such exact resolution gives one…
The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an…
We introduce a notion of residual diffeomorphism covariance in quantum Kantowski-Sachs (KS), describing the interior of a Schwarzschild black hole. We solve for the family of Hamiltonian constraint operators satisfying the associated…
With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions.…
We introduce two possible ways of defining effective constraints of quantum systems and applied this effective constraint method to models of WDW Quantum Cosmology and Loop Quantum Cosmology. We analyze effective Hamiltonian constraint on…