Related papers: Quantum Spacetime: a Disambiguation
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
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 formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
We propose an unexplored quantization method. It is based on the assumption of dynamical space-time intrinsic periodicities for relativistic fields, which in turn can be regarded as dual to extra-dimensional fields. As a consequence we…
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture…
It is argued that a noncommutative geometry of spacetime leads to a reconciliation of electromagnetism and gravitation while providing an underpinning to Weyl's geometry. It also leads to a cosmology consistent with observation. A few other…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
Quantum field planes furnish a noncommutative differential algebra $\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field…
We argue that the conventional construction for quantum fields in curved spacetime has a grave drawback: It involves an uncountable set of physical field systems which are nonequivalent with respect to the Bogolubov transformations, and…
We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In…