相关论文: Nonlinear distributional geometry and general rela…
In this work, standard methods of the mixed thin-shell foramlism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular…
An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes' Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a…
Alain Connes' noncommutative theory led to an interesting model including both Standard Model of particle physics and Euclidean Gravity. Nevertheless, an hyperbolic version of the gravitational part would be necessary to make physical…
I describe here some features of a non-geometrical approach to quantum gravity which leads to another picture of ties of gravitation and cosmology. The role of taking into account the effect of time dilation of the standard cosmological…
This work represents an application of constant mean curvature graphs (as solutions of the mean curvature PDE) to non-linear non-Darcy flows in porous media. It relates time invariant pressure distribution graphs to graphs of constant mean…
We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…
A review is given of some 2-dimensional metrics for which noncommutative versions have been found. They serve partially to illustrate a noncommutative extension of the moving-frame formalism. All of these models suggest that there is an…
We generalise the electric-magnetic duality in standard Maxwell theory to its non-commutative version. Both space-space and space-time non-commutativity are necessary. The duality symmetry is then extended to a general class of…
A recently proposed definition of a linear connection in non-commutative geometry, based on a generalized permutation, is used to construct linear connections on GL_q(n). Restrictions on the generalized permutation arising from the…
A summary of noncommutative spectral geometry as an approach to unification is presented. The role of the doubling of the algebra, the seeds of quantization and some cosmological implications are briefly discussed.
A classical Wilson line is a cooresponedce between closed paths and elemets of a gauge group. However the noncommutative geometry does not have closed paths. But noncommutative geometry have good generalizations of both: the covering…
The objective of this introduction to Colombeau algebras of generalized-functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic non-linear…
After a short discussion of the intimate relation between the generalized statistics and supersymmetry, we review the recent results on the nonlinear supersymmetry obtained in the context of the quantum anomaly problem and of the universal…
In this letter we reflect on the propagation of gravitational waves in alternative theories of gravity, which are typically formulated using extra gravitational degrees of freedom in comparison to General Relativity. We propose to…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
MSc thesis of the author offering an introduction to the operator algebraic approach to noncommutative geometry, with a treatment of some more advanced elements such as the noncommutative geometry of quantum groups, fuzzy physics, and…
We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by…
Exact plane gravitational radiation fields are presented within the framework of general relativity and their properties are described. The physics of nonlinear elliptically polarized plane gravitational waves is developed in close analogy…
The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…