Related papers: Born-Infeld Kinematics
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
One of the fundamental postulates of the special relativity theory is existence of a single system of universal coordinate transforms for inertial reference frames, that is coordinate transforms, which are uniquely determined by space-time…
The electric potential and the electromagnetic field for a linearly accelerated Born-Infeld charged particle are obtained in an inertial frame by a method that can, in principle, be applied to any electromagnetic theory. The method is based…
We give a brief account of supersymmetric Born-Infeld theories with extended supersymmetry, including those with partially broken supersymmetry. Some latest developments in this area are presented. One of them is N=3 supersymmetric…
We develop a Born-Infeld type theory for gravity in any dimension. We show that in four dimensions our formalism allows a self-dual (or anti-self dual) Born-Infeld gravity description. Moreover, we show that such a self-dual action is…
On the generalized tangent bundle of a smooth manifold, we study skew-symmetric endomorphism satisfying an arbitrary polynomial equation with real constant coefficients. We study the compatibility of these structures with the de Rham…
Deformed relativistic kinematics have been considered as a way to capture residual effects of quantum gravity. It has been shown that they can be understood geometrically in terms of a curved momentum space on a flat spacetime. In this…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
The subject of the paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicity and factorization properties of the…
We develop techniques of analyzing the unitarity of general Born-Infeld (BI) gravity actions in D-dimensional spacetimes. Determinantal form of the action allows us to find a compact expression quadratic in the metric fluctuations around…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It…
We construct an n-dimensional Born-Infeld type gravity theory that has the same properties as Einstein's gravity in terms of the vacuum and particle content: Namely, the theory has a unique viable vacuum (maximally symmetric solution) and a…
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…
The mathematical notion of foliated cobordism is presented, and its relationship to both the motion of extended particles and wave motion is detailed. The fact that wave motion, when represented in such a manner on a four-dimensional…
The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
We construct a tangent bundle exponential map and locally autoparallel coordinates for geometries based on a general connection on the tangent bundle of a manifold. As concrete application we use these new coordinates for Finslerian…
Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which…
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…