Related papers: Quantum de Sitter geometry
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
We present a survey of rigourous quantization results obtained in recent works on quantum free fields in de Sitter space. For the "massive'' cases which are associated to principal series representations of the de Sitter group SO\_0(1,4),…
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…
Using unitary irreducible representations of the de Sitter group, we construct the Fock space of a massive free scalar field. In this approach, the vacuum is the unique dS invariant state. The quantum field is a posteriori defined by an…
Open quantum systems interacting with the environments often show interesting behaviors, such as decoherence, non-unitary evolution, dissipation, etc. It is interesting but still challenging to study the open quantum gravitation system…
Quantum and classical physical states are represented in a unified way when they are described by symplectic tomography. Therefore this representation allows us to study directly the necessary conditions for a classical universe to emerge…
In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
We study the quantum dynamics of de Sitter space formulated as a minisuperspace model with flat spatial hypersurfaces in unimodular gravity, both in the Wheeler-DeWitt approach and in loop quantum cosmology (LQC). Time evolution is defined…
For a quantum field in a curved background the choice of the vacuum state is crucial. We exhibit a vacuum state in which the expectation values of the energy and pressure allow an intuitive interpretation. We apply this general result to…
We study some physical aspects of quantum field theory in a two stage universe starting from the inflationary de Sitter and transiting into the radiation dominated stage. We look into the time evolution of the primordial vacuum states,…
A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography or the dS/CFT correspondence. We show that de Sitter spacetime emerges from a free Sp(N) vector model by complexifying the ghost fields and flowing…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
We propose a theory of quantum gravity which formulates the quantum theory as a nonperturbative path integral, where each spacetime history appears with a weight given by the exponentiated Einstein-Hilbert action of the corresponding causal…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
We address the following question: To what extent can a quantum field tell if it has been placed in de Sitter space? Our approach is to use the techniques of non-equilibrium quantum field theory to compute the time evolution of a state…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first…