Related papers: Conformal Invariance and Wave-Particle Duality
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The…
Wave-particle duality is one of the fundamental properties of matter and at the same time, one of the mysteries of modern physics. In this paper, we propose and analyze a new interpretation of the wave-particle duality, and propose a new…
In this study, we use the concept of Bohmian trajectories to present a dynamical and deterministic interpretation for the gravity induced wave function reduction. We shall classify all possible regimes for the motion of a particle, based on…
Quantum mechanical boundary conditions along a timelike line, corresponding to the origin in radial coordinates, in two-dimensional dilaton gravity coupled to $N$ matter fields, are considered. Conformal invariance and vacuum stability…
The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented…
A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the…
Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two…
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…
Starting with the idea to describe phenomenologically the particle creation in the strong gravitational fields, we introduced explicitly the particle number nonconservation (= creation law) into the action integral with the corresponding…
We investigate several quantum phenomena related to quadratic gravity after rewriting the general fourth-order action in a more convenient form that is second-order in derivatives and produces only first-class constraints in phase space. We…
This article is based on the covariant causal set ($c$-causet) approach to discrete quantum gravity. A $c$-causet $x$ is a finite partially ordered set that has a unique labeling of its vertices. A rate of change on $x$ is described by a…
The traditional analysis of the basic version of the double-slit experiment leads to the conclusion that wave-particle duality is a fundamental fact of nature. However, such a conclusion means to imply that we are not only required to have…
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive…
We calculate the one-loop divergences for quantum gravity with cosmological constant, using new parametrization of quantum metric. The conformal factor of the metric is treated as an independent variable. As a result the theory possesses an…
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous…
External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…