Related papers: General reference frames and their associated spac…
In A. Poltorak's concept, the reference frame in General Relativity is a certain manifold equipped with a connection. The question under consideration here is whether it is possible to join two events in the space-time by a time-like…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Spacetime is modelled by binary relations - by the classes of the automorphisms $\GL(\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\U(2)$. In extension of Feynman propagators for particle…
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…
We provide a discussion about the necessity to fix the reference frame before quantizing the gravitational field. Our presentation is based on stressing how the 3+1-slicing of the space time becomes an ambiguous procedure as referred to a…
Reference frames are used to parameterize measurements of physical effects, but since their practical realization uses material objects, they may affect observations performed in a combined quantum state of the measured system together with…
A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…
We show how a suitably prepared set of clocks can be used to determine all components of the gravitational field in General Relativity. We call such an experimental setup a clock compass, in analogy to the usual gravitational compass.…
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…
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 study Heisenberg's uncertainty relation relative to a quantum reference frame (QRF). We introduce the QRF as a covariant phase-space observable, show that when described relative to it, position and momentum appear compatible, and derive…
Some aspects of quantum field theory in a general (i.e. non inertial) frame of Minkowski spacetime are studied. Conditions for the presence of horizons as well as for the modification of the definition of positive energy solutions are…
Gravity is understood as a geometrization of spacetime. But spacetime is also the manifold of the boundary values of the spinless point particle in a variational approach. Since all known matter, baryons, leptons and gauge bosons are…
A reference frame in event space is a smooth field of orthonormal bases. Every reference frame is equipped by anholonomic coordinates. Using anholonomic coordinates allows to find out relative speed of two observers and appropriate Lorentz…
In a background independent theory without boundary, physical observables may be defined with respect to dynamical reference systems. However, I argue here that there may be a symmetry that exchanges the degrees of freedom of the physical…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group G on a space E. We…
Spacetime is modelled as a homogeneous manifold given by the classes of unitary $\U(2)$ operations in the general complex operations $\GL(\C^2)$. The residual representations of this noncompact symmetric space of rank two are characterized…