Related papers: Quantum de Sitter geometry
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
We consider quantum field theory in de Sitter space, focusing on the cases of scalars, spin 1/2 fields, and symmetric and anti-symmetric tensor fields of arbitrary spin. The free field equations in global coordinates can be reduced to a one…
The concept of quantum geometry for single-particle states has revolutionized our interpretation of several emergent properties in condensed matter. However, a description of the quantum geometry for interacting particles and an…
We consider the quantum description of a toy model universe in which the Schwarzschild-de Sitter geometry emerges from the coherent state of a massless scalar field. Although highly idealised, this simple model allows us to find clear hints…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
If one tries to view de Sitter as a true (as opposed to a meta-stable) vacuum, there is a tension between the finiteness of its entropy and the infinite-dimensionality of its Hilbert space. We invetsigate the viability of one proposal to…
Understanding the geometric information contained in quantum states is valuable in various branches of physics, particularly in solid-state physics when Bloch states play a crucial role. While the Fubini-Study metric and Berry curvature…
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…
The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes…
In de Sitter ambient space formalism, the linear gravity can be written in terms of a minimally coupled scalar field and a polarization tensor. In this formalism, the massless minimally coupled scalar field can be quantized on Bunch-Davies…
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
We perform a foliation of a four dimensional Riemannian space-time with respect to a discrete time which is an integer multiple of the Planck time. We find that the quantum fluctuations of the metric have a discrete energy spectrum. The…
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…