Related papers: Projective Loop Quantum Gravity I. State Space
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…
In a seminal paper, Kaminski, Kisielowski an Lewandowski for the first time extended the definition of spin foam models to arbitrary boundary graphs. This is a prerequisite in order to make contact to the canonical formulation of Loop…
Quantization identifies the cotangent bundle of projective space with the (non-Hermitian) rank-$1$ projections of a Hilbert space. We use this identification to study the natural geometric structures of these cotangent bundles and those of…
Nowadays projective quantum states can be constructed for a number of field theories including Loop Quantum Gravity. However, these states are kinematic in this sense that their construction does not take into account the dynamics of the…
We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum…
The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix $\{\hg_{ab}(x)\}$ composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with…
In a quantum mechanical treatment of gauge theories (including general relativity), one is led to consider a certain completion, $\agb$, of the space $\ag$ of gauge equivalent connections. This space serves as the quantum configuration…
We introduce a master constraint operator on the kinematical Hilbert space of loop quantum gravity representing a set of gauge conditions which classically fix the densitized triad to be diagonal. We argue that the master constraint…
Quantum probability provides a novel framework for formulating machine-learning (ML) problems in Hilbert space. We introduce a prototype-based learning scheme where class representatives are encoded as generative matrix product states…
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…
We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states…
Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this…
The study of dualities is a central issue in several modern approaches to quantum field theory, as they have broad consequences on the structure and on the properties of the theory itself. We call Abelian duality the generalisation to…
This work seeks to make explicit the operational connection between the preparation of two-level quantum systems with their corresponding description (as states) in a Hilbert space. This may sound outdated, but we show there is more to this…
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked…
The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables…
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…
A new type of gauge quantum theory (superrelativity) has been proposed. This differs from ordinary gauge theories in sense that the affine connection of our theory is constructed from first derivatives of the Fubini-Study metric tensor.…