Related papers: Quantum Roots in Geometry: II
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
One of the biggest challenges to theoretical physics of our time is to find a background-independent quantum theory of gravity. Today one encounters a profusion of different attempts at quantization, but no fully accepted - or acceptable,…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
The parity operator $\cal P$ and time reversal operator $\cal T$ are two important operators in the quantum theory, in particular, in the $\cal PT$-symmetric quantum theory. By using the concrete forms of $\cal P$ and $\cal T$, we discuss…
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…
Current theories of particle physics, including the standard model, are dominated by the paradigm that nature is basically translation invariant. Deviations from translation invariance are described by the action of forces. General…
We present a new geometry of spacetime where events may be positive dimensional. This geometry is obtained by applying the identity of indiscernibles, which is a fundamental principle of quantum statistics, to time. Quantum nonlocality…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism within the framework of information geometry. In this paper, we formulate a correspondence…
In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge invariant Hilbert space of loop quantum gravity. It is shown that the reduced…
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
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…
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the…
With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
In this work we provide a possible geometrical interpretation of the spin of elementary particles. In particular, it is investigated how the wave equations of matter are altered by the addition of an antisymmetric contribution to the metric…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…