Related papers: Generalized Doppler effect in spaces with a transp…
In this work we experimentally demonstrate the quantum interference of force effect using pairs of entangled photons. Although photons are massless particles, they have linear momentum, and our experiments show that the quantum…
In this paper we introduce a notion of parallel transport for principal bundles with connections over differentiable stacks. We show that principal bundles with connections over stacks can be recovered from their parallel transport thereby…
A linear F-manifold is an F-manifold (E, \circ , e) defined on the total space of a vector bundle \pi : E \rightarrow M for which the multiplication and unit field are linear tensor fields. We develop a systematic treatment of linear…
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on…
Semigroup algebras admit certain `coherent' deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave…
We consider the propagation of two-photon light in a random medium. We show that the Wigner distribution of the two-photon wave function obeys an equation that is analogous to the radiative transport equation for classical light. Using this…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
The difficulties with which the concept of point-like particles is beset, such as the infinities encountered in the existing theories of elementary particles, suggest a different approach to the study of these particles. Instead of…
In the context of special relativity, we describe with detail the Doppler effect between a light source at rest and an observer in linear motion and constant proper acceleration. To have an Englis version of this article, ask the authors.…
Recently, Li and Liu have studied global monoole of tachyon in a four dimensional static space-time. We analyze the motion of massless and massive particles around tachyon monopole. Interestingly, for the bending of light rays due to…
Nature allows one to explore a manifold of remarkable quantum effects. Most prominently, quantum entanglement can be observed in many-particle systems, between multiple quantized fields, and in hybrid combinations thereof. This diversity,…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We study the mixing of photons with hypothetical massive spin-two particles in the presence of a magnetic field. Mixing phenomena have been studied in the case of axion-like particles and strictly massless spin-two particles (gravitons) but…
We analyse the massless wave equation on a class of two dimensional manifolds consisting of an arbitrary number of topological cylinders connected to one or more topological spheres. Such manifolds are endowed with a degenerate…
The aim of this paper is to re-examine the question of the average magnification in a universe with some inhomogeneously distributed matter. We present an analytic proof, valid under rather general conditions, including clumps of any shape…
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we…
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
Quantized space described by time reversal invariant and rotationally invariant noncommutative algebra of canonical type is studied. A particle in uniform field is considered. We find exactly the energy of a particle in uniform field in the…
A null path in 5D can appear as a timelike path in 4D, and for a certain gauge in 5D the motion of a massive particle in 4D obeys the usual quantization rule with an uncertainty-type relation. Generalizations of this result are discussed in…