相关论文: On the Minkowski-Funk Transform

We define the notion of weak Minkowski metric and prove some basic properties of such metrics. We also highlight some of the important analogies between Minkowski geometry and the Funk and Hilbert geometries.

Based on a mechanism originally suggested for causal fermion systems, the present paper paves the way for a rigorous treatment of baryogenesis in the language of differential geometry and global analysis. Moreover, a formula for the rate of…

In this work we study weighted Radon transforms in multidimensions. We introduce an analog of Chang approximate inversion formula for such transforms and describe all weights for which this formula is exact. In addition, we indicate…

The Minkowski functionals are a mathematical tool to quantify morphological features of patterns. Some applications to the matter distribution in galaxy catalogues and N-body simulations are reviewed, with an emphasis on the effects of…

The quantization of gravitational waves in the Milne universe is discussed. The relation between positive frequency functions of the gravitational waves in the Milne universe and those in the Minkowski universe is clarified. Implications to…

A Minkowski class is a closed subset of the space of convex bodies in Euclidean space Rn which is closed under Minkowski addition and non-negative dilatations. A convex body in Rn is universal if the expansion of its support function in…

In this overview article we present a formalism suitable for constructing models of QFT's on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the standard QFT…

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line…

We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we…

Here we develop a general theory of mode transformation (diffraction) at the flat transverse boundary between cold magnetized electron plasma and isotropic vacuum-like medium inside a circular waveguide. The obtained results can be also…

The role of the quantum universal enveloping algebras of symmetries in constructing non-commutative geometry of the space-time including vector bundles, measure, equations of motion and their solutions is discussed. In the framework of the…

We introduce a new family of invariant differential operators associated with $\lambda$-cosine and Funk-Radon transforms on Stiefel and Grassmann manifolds. These operators reduce the order of the $\lambda$-cosine transforms and yield new…

A Fourier transform from momentum space to twistor space is introduced in twistor string theory, for the first time, for the case where the twistor space is a three-dimensional real projective space, corresponding to ultra-hyperbolic…

A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…

We present a pedagogical description of the inversion of Gamow's tunnelling formula and we compare it with the corresponding classical problem. We also discuss the issue of uniqueness in the solution and the result is compared with that…

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

This paper is an introductory text to the theory of $q$-deformed Fourier transforms, as first discussed by Rogov and Olshanetsky. We derive the well-known results in detail, present them in a format that suits our needs, and include some…

Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical…

An attempt is made of giving a self-contained (although incomplete) introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component…

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…