Geometry of the quantum universe

A quantum universe with the global shape of a (Euclidean) de Sitter spacetime appears as dynamically generated background geometry in the causal dynamical triangulation (CDT) regularisation of quantum gravity. We investigate the micro- and macro-geometry of this universe, using geodesic shell decompositions of spacetime. More specifically, we focus on evidence of fractality and global anisotropy, and on how they depend on the bare coupling constants of the theory.     

Time in quantum cosmology from the self-measurement of the universe

This essay received the fourth award from the Gravity Research Foundation, 1990 — Ed.     

The creation of the universe as a quantum phenomenon

Quantum creation of massy particles can occur in the cosmological context without cost of energy. This fact is seized upon to construct a causal open homogeneous isotropic cosmology. The universe is conceived as the response of matter and the gravitational field to a spontaneous pointlike disturbance. Its history unfolds in two stages, creation and free expansion. The first stage gives rise to a “fireball.” The free expansion is extrapolated back to the “fireball.” The latter thus replaces the “big-bang,” thereby avoiding an initial singularity. Though not intrinsic to the theory it does suggest the interpretation of the cosmological part of the gravitational field as the scalar dilaton that is encountered in the dynamical generation of mass in conformally invariant theory.     

The transfer of the quantum correlation from two-mode nonclassical state field to the supercurrents in two distant SQUID rings

We have considered two distant mesoscopic superconducting quantum interference device (SQUID) rings A and B in the presence of two-mode nonclassical state fields and investigated the correlation of the supercurrents in the two rings using the normalized correlation function $C_{\rm AB}$. We show that when the parameter $\alpha$ is very small for the separable state with the density matrix $\hat {\rho } = (\left| {\alpha , - \alpha } \right\rangle \left\langle {\alpha , - \alpha } \right| + \left| { - \alpha ,\alpha } \right\rangle \left\langle { - \alpha ,\alpha } \right|) / 2$ and entangled coherent state (ECS) $\left| u \right\rangle = N_1 (\left| {\alpha , - \alpha } \right\rangle + \left| { - \alpha ,\alpha } \right\rangle )$ fields, the dynamic behaviours of the normalized correlation function $C_{\rm AB}$ are similar, but it is quite different for the entangled coherent state $\left| {u}' \right\rangle = N_2 (\left| {\alpha , - \alpha } \right\rangle - \left| { - \alpha ,\alpha } \right\rangle )$ field. When the parameter $\alpha $ is very large, the dynamic behaviours of $C_{\rm AB}$ are almost the same for the separable state, entangled coherent state $\left| u \right\rangle $ and $\left| {u}' \right\rangle $ fields. For the two-mode squeezed vacuum state field the maximum of $C_{\rm AB}$ increases monotonically with the squeezing parameter $r$, and as $r \to \infty $, $C_{\rm AB} \to 1$. This means that the supercurrents in the two rings A and B are quantum mechanically correlated perfectly. It is concluded that not all the quantum correlations in the two-mode nonclassical state field can be transferred to the supercurrents; and the transfer depends on the state of the two-mode nonclassical state field prepared.     

Quantum correlation of a three-particle-class state under quantum decoherence

We investigate the quantum characteristics of a three-particle W-class state and reveal the relationship between quantum discord and quantum entanglement under decoherence.We can also identify the state for which discord takes a maximal value for a given decoherence factor,and present a strong bound on quantum entanglement–quantum discord.In contrast,a striking result will be obtained that the quantum discord is not always stronger than the entanglement of formation in the case of decoherence.Furthermore,we also theoretically study the variation trend of the monogamy of quantum correlations for the three-particle W-class state under the phase flip channel,and find that the three-particle W-class state could transform from polygamous into monogamous,owing to the decoherence.     

Towards the deformation quantization of linearized gravity

We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell Lagrangian which allows the construction of a Hamiltonian in the standard way. The deformation quantization procedure for free fields is applied to this Hamiltonian. As a result we obtain the complete set of quantum states and the discrete energy spectrum of linearized gravity.     

Getzler symbol calculus and deformation quantization

In this paper we give a construction of Fedosov quantization incorporating the odd variables and an analogous formula to Getzler’s pseudodifferential calculus composition formula is obtained. A Fedosov type connection is constructed on the bundle of Weyl tensor Clifford algebras over the cotangent bundle of a Riemannian manifold. The quantum algebra associated with this connection is used to define a deformation of the exterior algebra of Riemannian manifolds.     

Wave packets for the quantum Kantowski-Sachs universe

Some quantum Kantowski-Sachs minisuperspace models are studied. It is shown that a good classical limit can be constructed. However, the discussed solutions do not remove the singularities of the models.     

High-energy quantum mechanics and dynamical quantization

A generalization of quantum mechanics is developed for the one-particle one-dimensional case. The position operator eigenvalues, i.e. the physical space, are determined by the energy in our approach. Some of the results obtained are reminiscent of experimental facts characteristic of high-energy physics.     

Mach's principle. Part 1. Initial state of the universe the universe

The integral formulation of equations of general relativity proposed earlier as a mathematical tool for Mach's principle forbids the conventional singular cosmologies but is compatible with the de Sitter initial space.     

Induced spin interactions in the early universe from discrete time quantum theory

By considering a system of spinning particles in an external magnetic field we demonstrate that the system develops non-local spin interactions due to discrete time quantum effects. Such interactions can lead to a domain like structure in the early universe possibly serving as generic seeds to large scale structure.     

Quantum correlation of a three-particle W-class state under quantum decoherence

We investigate the quantum characteristics of a three-particle W-class state and reveal the relationship between quan- tum discord and quantum entanglement under decoherence. We can also identify the state for which discord takes a maximal value for a given decoherence factor, and present a strong bound on quantum entanglement-quantum discord. In contrast, a striking result will be obtained that the quantum discord is not always stronger than the entanglement of formation in the case of decoherence. Furthermore, we also theoretically study the variation trend of the monogamy of quantum correlations for the three-particle W-class state under the phase flip channel, and find that the three-particle W-class state could transform from polygamous into monogamous, owing to the decoherence.