Related papers: Positive Geometries and Differential Forms with No…
We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the…
We classify projective toric manifolds whose dual variety is not a hypersurface in the dual projective space. Under the standard dictionary between toric geometry and convex geometry, they correspond to certain convex Delzant integer…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
A realistic analysis shows that constraining a quantomechanical system produces the effective dynamics to be coupled with {\sl abelian/non-abelian gauge fields} and {\sl quantum potentials} induced by the {\sl intrinsic} and {\sl extrinsic…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge…
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…
Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a Mathematica package called…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many…
Orthogonal spaces are vector spaces together with a quadratic form whose associated bilinear form is non-degenerate. Over fields of characteristic two, there are many quadratic forms associated to a given bilinear form and quadratic…
The so-called Scattering Equations which govern the kinematics of the scattering of massless particles in arbitrary dimensions have recently been cast into a system of homogeneous polynomials. We study these as affine and projective…
Many physical systems are described by partial differential equations (PDEs). Determinism then requires the Cauchy problem to be well-posed. Even when the Cauchy problem is well-posed for generic Cauchy data, there may exist characteristic…
A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator,…
The aim of this work is to construct examples of pairs whose logarithmic cotangent bundles have strong positivity properties. These examples are constructed from any smooth n-dimensional complex projective varieties by considering the sum…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (its complement in 3-space), and dimension four (the moduli…
In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and…
In this paper we systematically study a five-parameters class of spherically symmetric polymer black/white hole solutions, and find that only three independent combinations are physical and uniquely determine the spacetime properties. After…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…