Related papers: Quantum Kaluza-Klein theory with $M_2(\mathbb{C})$
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…
We discuss some of the issues to be addressed in arriving at a definitive noncommutative Riemannian geometry that generalises conventional geometry both to the quantum domain and to the discrete domain. This also provides an introduction to…
We consider the following generalisation of a well-known problem in Riemannian geometry: When is a smooth real-valued function s on a given compact n-dimensional manifold M (with or without boundary) the scalar curvature of some smooth…
The Coleman-Mandula (CM) theorem states that the Poincar\'e and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field…
Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome.…
We introduce partial secondary invariants associated to complete Riemannian metrics which have uniformly positive scalar curvature outside a prescribed subset on a spin manifold. These can be used to distinguish such Riemannian metrics up…
We present a detailed description of a quantum scalar field theory within a flat spacetime confined to a cavity with perfectly reflecting moving boundaries. Moreover, we establish an equivalence between this time-dependent setting and a…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
We study a six-dimensional Kaluza-Klein theory with spacetime topology $M_4 \times S^2$ and analyze the gauge sector arising from dimensional reduction. Using normalized Killing vectors on $S^2$, we explicitly construct the reduced…
Applying the G_{2(2)} generating technique for minimal D=5 supergravity to the Rasheed black hole solution, we present a new rotating charged Kaluza-Klein black hole solution to the five-dimensional Einstein-Maxwell-Chern-Simons equations.…
We apply a recent proposal for defining states and observables in quantum gravity to simple models. First, we consider a Klein-Gordon particle in an ex- ternal potential in Minkowski space and compare our proposal to the theory ob- tained…
We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space…
Let $(M,g)$ and $(K,\kappa)$ be two Riemannian manifolds of dimensions $m$ and $k ,$ respectively. Let $\omega\in C^2(N),$ $\omega> 0.$ The warped product $ M\times _\omega K$ is the $ (m+k)$-dimensional product manifold $M\times K$…
The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
We construct a unified covariant derivative that contains the sum of an affine connection and a Yang-Mills field. With it we construct a lagrangian that is invariant both under diffeomorphisms and Yang-Mills gauge transformations. We assume…
In this paper, the basic quantum field equations of free particle with 0-spin, 1-spin (for case of massless and mass $>$ 0) and 1/2 spin are derived from Einstein equations under modified Kaluza-Klein metric, it shows that the equations of…
We study the quantum cosmology of an empty (4+1)-dimensional Kaluza-Klein cosmology with a negative cosmological constant and a FRW type metric with two scale factors, one for 4-D universe and the other for one compact extra dimension. By…