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A fundamental task in any physical theory is to quantify certain physical quantity in a meaningful way. In this paper we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding…

We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…

I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…

We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…

The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose…

Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs…

We study the deformation (Moyal) quantisation of gravity in both the ADM and the Ashtekar approach. It is shown, that both can be treated, but lead to anomalies. The anomaly in the case of Ashtekar variables, however, is merely a central…

A recent debate has ensued over the claim by Pikovski et al. [Nat. Phys. 11, 668 (2015)] that systems with internal degrees of freedom undergo a universal, gravity-induced, type of decoherence that explains their quantum-to-classical…

The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…

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…

A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…

This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity…

Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the…

The Ashtekar variables have been use to find a number of exact solutions in quantum gravity and quantum cosmology. We investigate the origin of these solutions in the context of a number of canonical transformations (both complex and real)…

In order to perform accurate and stable long-term numerical integration of the Einstein equations, several hyperbolic systems have been proposed. We here report our numerical comparisons between weakly hyperbolic, strongly hyperbolic, and…

Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability…

We investigate the role of external constraints in quantum field theory using the path integral formalism. We begin by reviewing the quantization of constrained systems and extend the analysis to cases where constraints are added to the…

A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections in the quantum dynamics governing many-particle systems in a gravitational field. Here we…

We revisit the calculation of quantum-gravitational corrections to the power spectra of scalar and tensor perturbations in the Born-Oppenheimer approach to quantum gravity. We focus on the issue of the definition of the inner product of the…

Relationalism -- along the lines developed by Barbour and collaborators in the past 3 decades -- can be considered an advance with 1/4 of the facets of the canonical approach's Problem of Time as identified by Isham and Kuchar. Indeed,…