Related papers: On the force fields which are homogeneous of degre…
In the SU(2)_{L} x U(1)_{Y} standard electroweak theory coupled with the Einstein gravity, new topological configurations naturally emerge, if the spatial section of the universe is globally a three-sphere(S^3) with a small radius. The…
We define `third derivative' General Relativity, by promoting the integration measure in Einstein-Hilbert action to be an arbitrary $4$-form field strength. We project out its local fluctuations by coupling it to another $4$-form field…
In this paper, it is proved that any conformal vector field is homothetic on a locally projectively flat $(\alpha,\beta)$-space of non-Randers type in dimension $n\ge 3$, and the local solutions of such a vector field are determined. While…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models including the Hilbert-Einstein curvature term…
A classical problem of mechanics involves a projectile fired from a given point with a given velocity whose direction is varied. This results in a family of trajectories whose envelope defines the border of a 'safe' domain. In the simple…
We undertake a novel approach to the existence problem for gravitating vortices on a Riemann surface based on symplectic reduction by stages, which seems to be new in the PDE as well as the gauge theory literature. The main technical tool…
In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces, reducing the system to a collection of (D-n)-dimensional fields. This allows one…
We consider degree-d forms on the Euclidean unit sphere. We specialize to our setting a genericity result by Nie obtained in a more general framework. We exhibit an homogeneous polynomial Res in the coefficients of f , such that if Res(f) =…
Using the language of differential forms, the Kaluza-Klein theory in 4+1 dimensions is derived. This theory unifies electromagnetic and gravitational interactions in four dimensions when the extra space dimension is compactified. Without…
The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of few atomically thick layers and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced…
Optimizing the free energy under a mass constraint may generate a convex crystal subject to assumptions on the potential $g(0)=0$, $g \ge 0$. The general problem classically attributed to Almgren is to infer if this is the case assuming the…
We study the possibility that a generalised real scalar field minimally coupled to gravity could explain both the galactic and the cosmological dark components of the universe. Within the framework of Einstein's Relativity we model static…
Regularization of damped motion under central forces in two and three-dimensions are investigated and equivalent, undamped systems are obtained. The dynamics of a particle moving in $\frac{1}{r}$ potential and subjected to a damping force…
We study the possible existence of a Newtonian regime of gravity in $1+1$ dimensions, considering metrics in both the Kerr-Schild and conformal forms. In the former case, the metric gives the exact solution of the Poisson equation in flat…
On a compact complex affine manifold with a constant coefficient K\"ahler metric $\omega_0$, we introduce a concept: $(S,\omega_0)$-convexity and show that $(S,\omega_0)$-convexity is preserved by geodesics in the space of K\"ahler…
In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
In the case of one extra dimension, well known Newton's potential $\phi (r_3)=-G_N m/r_3$ is generalized to compact and elegant formula $\phi(r_3,\xi)=-(G_N m/r_3)\sinh(2\pi r_3/a)[\cosh(2\pi r_3/a)-\cos(2\pi\xi/a)]^{-1}$ if…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…