Related papers: Conserved quantities in isotropic loop quantum cos…
The concept of effective dynamics has proven successful in LQC, a loop-inspired quantization of cosmological spacetimes. We apply the same idea of its derivation in LQC to the full theory, by computing the expectation value of the scalar…
We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy…
The algebra of observables of $SO_{q}(3)$-symmetric quantum mechanics is extended to include the inverse $\frac{1}{R}$ of the radial coordinate and used to obtain eigenvalues and eigenfunctions of a \q-deformed Coulomb Hamiltonian.
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to…
The evolution of the black hole horizon can be effectively captured by a fictitious membrane fluid living on the stretched horizon. We show that the dynamics of this boundary matter arises from the invariance of the bulk action under local…
An analytical approach for studying the cosmological scenario with a homogeneous tachyon field within the framework of loop quantum gravity is developed. Our study is based on the semi-classical regime where space time can be approximated…
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…
We discuss the semiclassical limit of Quantum Reduced Loop Gravity, a recently proposed model to address the quantum dynamics of the early Universe. We apply the techniques developed in full Loop Quantum Gravity to define the semiclassical…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
We extend the treatment of quantum cosmology to a manifold with torsion. We adopt a model of Einstein-Cartan-Sciama-Kibble compatible with the cosmological principle. The universe wavefunction will be subject to a $\mathcal{PT}$-symmetric…
We apply the nonstandard loop quantum cosmology method to quantize a flat Friedmann-Robertson-Walker cosmological model with a free scalar field and the cosmological constant $\Lambda>0$. Modification of the Hamiltonian in terms of loop…
In a previous work and in terms of an exact quantum-mechanical framework, $\hbar$-independent causal and retarded expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge were derived in the presence of a…
It is shown that several prescriptions for the effective continuum limit of the flat Friedmann-Lemaitre-Robertson-Walker loop quantum cosmology can be understood as the exact classical limit of the Wheeler-DeWitt quantization of certain…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
The entropy of a classical thermally isolated Hamiltonian system is given by the logarithm of the measure of phase space enclosed by the constant energy hyper-surface, also known as volume entropy. It has been shown that on average the…
We analyse the semi-classical and quantum dynamics of the isotropic Universe in the framework of the Polymer Quantum mechanics, in order to implement a cut-off physics on the initial singularity. We first identify in the Universe cubed…
The longstanding issue of general covariance in effective models of quantum gravity is addressed, which arises when canonical quantum gravity leads to a semiclassical model described by an effective Hamiltonian constraint. In the context of…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
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…