Related papers: Shape Quantities for Relational Quadrilateralland
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
A modified version of the bilocal particle is presented in terms of complex space time. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac's conjecture.…
In this paper I give overviews of the polysymplectic approach to covariant Hamiltonian field theory and the simplest geometric quantization of classical particle theories. I then give a synopsis of a recently proposed toy model for applying…
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
There is a vast literature showing the connection between a deformed relativistic kinematics and a curved momentum space, and, in particular, how the former can be obtained from the geometrical properties of the latter. However, there is…
In this paper we investigate the history of relationalism and its present use in some interpretations of quantum mechanics. In the first part of this article we will provide a conceptual analysis of the relation between substantivalism,…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
In this article I elaborate on the approach to relational quantum mechanics suggested by Adlam and Rovelli (2023). I suggest that this approach fills an important gap in the spectrum of relational approaches, because it posits that the…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
A central aim of theoretical physics is to account for the structure of matter at the most elementary level as underlying the Standard Model of particle physics, and ideally also as a basis for a substantial dark sector, as distributed in…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories,…
Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.
This article contains a local solution to the notorious Problem of Time in Quantum Gravity at the conceptual level and which is actually realizable for the relational triangle. The Problem of Time is that `time' in GR and `time' in ordinary…
Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
In quantum mechanics, spatial correlations arising from measurements at separated particles are well studied. This is not the case, however, for the temporal correlations arising from a single quantum system subjected to a sequence of…
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,…
Up to now it has been impossible to find a realistic interpretation for the reduction process in relativistic quantum mechanics. The basic problem is the dependence of the states on the frame within which collapse takes place. A suitable…