Related papers: Invariants in Quantum Geometry
Why are "analogue spacetimes'' interesting? For the purposes of this workshop the answer is simple: Analogue spacetimes provide one with physically well-defined and physically well-understood concrete models of many of the phenomena that…
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to…
Viewing frames of reference as physical systems, subject to the same laws as the systems they describe, is central to the relational approach in physics. Under the assumption that quantum mechanics universally governs all physical entities,…
In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of…
In this paper, we study implications of the geometrical nature of space- time for some of the basic tenets of quantum mechanics. That is, we study two different implications of the principle of general covariance; first we quantize a…
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In this work, we explore these notions in the context of quantum reference frame (QRF) covariance, in…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…
We review the recent developments of quantum invariants of 3-manifolds and links: $\hat{Z}$ and $F_L$. They are $q$-series invariants originated from mathematical physics. They exhibit rich features, for example, quantum modularity,…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
Quantum relativity as a generalized, or rather deformed, version of Einstein relativity with a linear realization on a classical six-geometry beyond the familiar setting of space-time offer a new framework to think about the quantum…
In the past decade the phenomenology of quantum gravity has been dominated by the search of violations of Lorentz invariance. However, there are very serious arguments that led us to assume that this invariance is a symmetry in Nature. This…
Challenging Mermin's perspective that ``correlations have physical reality; that which they correlate does not'' we argue that correlations and correlata are not fundamentally distinct. These are dual concepts depending on the tensor…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector…
This article presents a precise description of the interplay between the symmetries of a quantum or classical theory with spacetime interpretation, and some of its physical properties relating to causality, horizons and positive energy. Our…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
The present thesis deals with some properties of classical and quantum scalar fields in an inhomogeneous and/or time-dependent background, focusing on models where the latter can be described as a curved space-time with an event horizon.…