Related papers: Consistency Check on Volume and Triad Operator Qua…
2+1 gravity coupled to a massless scalar field has an initial singularity when the spatial slices are compact. The quantized model is used here to investigate several issues of quantum gravity. The spectrum of the volume operator is studied…
We re-examine the process of loop quantization for flat isotropic models in cosmology. In particular, we contrast different inequivalent `loop quantizations' of these simple models through their respective successes and limitations and…
In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a…
The Mollow triplet is a fundamental signature of quantum optics, and has been observed in numerous quantum systems. Although it arises in the 'strong driving' regime of the quantized field, where the atoms undergo coherent oscillations, it…
The intention of this thesis is to provide general tools and concepts that allow to perform a mathematically substantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum…
The logarithm function is the gravitational potential in $\mathbb{R}^2$. We prove that the logarithm central force problem is block regularizable, that is, the (incomplete) flow may be continuously extended over the singularity at the…
Loop Quantum Gravity (LQG) is one of the leading approaches to unify quantum physics and General Relativity (GR). The Hilbert space of LQG is spanned by spin-networks which describe the local geometry of quantum space-time. Simulation of…
This paper investigates the mathematical nature of qualitative uncertainty principle (QUP), which plays an important role in mathematics, physics and engineering fields. Consider a 3-tuple (K, H1, H2) that K: H1 -> H2 is an integral…
Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
We give a prescription to define in Loop Quantum Gravity the electric field operator related to the scale factor of an homogeneous and isotropic cosmological space-time. This procedure allows to link the fundamental theory with its…
We show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
A consistent implementation of quantum gravity is expected to change the familiar notions of space, time and the propagation of matter in drastic ways. This will have consequences on very small scales, but also gives rise to correction…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…