Related papers: On a Lattice-Independent Formulation of Quantum Ho…
A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general…
With a well-motivated extension of higher order holonomy corrections, the quantum theory of loop quantum cosmology (LQC) for the $k=0$ Friedmann-Robertson-Walker model (with a free massless scalar) is rigorously formulated. The analytical…
We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
We take a step towards the non-perturbative description of a two-dimensional dilaton-gravity theory which has a vanishing cosmological constant and contains black holes. This is done in terms of a double-scaled Hermitian random matrix model…
The Hamilton function is a powerful tool for studying the classical limit of quantum systems, which remains meaningful in background-independent systems. In quantum gravity, it clarifies the physical interpretation of the transitions…
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
The present paper is the companion of [1] in which we proposed a scheme that tries to derive the Quantum Field Theory (QFT) on Curved Spacetimes (CST) limit from background independent Quantum General Relativity (QGR). The constructions of…
There is a precise sense in which the requirement of background independence suffices to uniquely select the kinematics of loop quantum gravity (LQG). Specifically, the fundamental kinematic algebra of LQG admits a unique diffeomorphism…
We propose a scheme leading to a non-perturbative definition of lattice field theories which are scale-invariant on the quantum level. A key idea of the construction is the replacement of the lattice spacing by a propagating dynamical field…
QCD is constructed as a lattice gauge theory in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. The resulting quantum link model for QCD is formulated with a fifth Euclidean…
Loop Quantum Gravity heavily relies on a connection formulation of General Relativity such that 1. the connection Poisson commutes with itself and 2. the corresponding gauge group is compact. This can be achieved starting from the Palatini…
The number state method is used to study soliton bands for three anharmonic quantum lattices: i) The discrete nonlinear Schr\"{o}dinger equation, ii) The Ablowitz-Ladik system, and iii) A fermionic polaron model. Each of these systems is…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We…
The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a…
In the framework of loop quantum cosmology anomaly free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of the construction in (non-symmetric) loop…
Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in a non-perturbative treatment of the quantum…
Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It, therefore,…