Related papers: Quantum Kaluza-Klein theory with $M_2(\mathbb{C})$
We examine a charged scalar field with a position-dependent mass \( m(\rho) = m_0 + \mathcal{S}(\rho) \), where \(\mathcal{S}(\rho)\) represents a Lorentz scalar potential, near a BTZ black hole in the presence of an external magnetic…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…
In this paper we consider the Kaluza-Klein fields equations in presence of a generic 5D matter tensor which is governed by a conservation equation due to 5D Bianchi identities. Following a previous work, we provide a consistent approach to…
In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions. We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
We construct pairs of compact K\"ahler-Einstein manifolds $(M_i,g_i,\omega_i)$ ($i=1,2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_i=\bigwedge^n T^*M_i$ has Chern class $[\omega_i/2\pi]$, and for…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
We quantize the interaction of gravity with a Yang-Mills and Higgs field using canonical quantization. Similar to the approach in a previous paper we discard the Wheeler-DeWitt equation and express the Hamilton constraint by the evolution…
Let $(\MM ,{\tilde g})$ be an $N$-dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen-Cahn equation $$ \epsilon^2\Delta_{ {\tilde g}} {u}\,+\, (1 - {u}^2)u \,=\,0\quad \mbox{in } \MM, $$ where…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
The idea of extra dimensions provides a promising approach to overcome various problems in modern physics. This includes theoretical as well as phenomenological aspects, such as the unification of the fundamental interactions or the…
In this paper we establish new Calabi-Bernstein results for maximal surfaces immersed into a Lorentzian product space of the form $M^2\times\mathbb{R}_1$, where $M^2$ is a connected Riemannian surface and $M^2\times\mathbb{R}_1$ is endowed…
Within the so-called group geometric approach to (super)gravity and (super)string theories, any compact Lie group manifold $G_{c}$ can be smoothly deformed into a group manifold $G_{c}^{\mu }$ (locally diffeomorphic to $G_{c}$ itself),…
Let $M$ be pseudo-Riemannian homogeneous Einstein manifold of finite volume, and suppose a connected Lie group $G$ acts transitively and isometrically on $M$. In this situation, the metric on $M$ induces a bilinear form…
We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system.…
An exact solution of the source-free Kaluza-Klein field equations is presented. It is a 5D generalization of the Robinson-Trautman quasi-spherical gravitational wave with a cosmological constant. The properties of the 5D solution are…
In a Friedmann-Robertson-Walker (FRW) space-time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the…
Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…
The quantum cohomology of Grassmannians exhibits two symmetries related to the quantum product, namely a \Bbb {Z}/n action and an involution related to complex conjugation. We construct a new ring by dividing out these symmetries in an…