Dual gravitation of relativistic particles

Abstract

The usual gravitation theories, like Newton´s non-relativistic theory of gravitation and Einstein´s relativistic one, are based on the concept of gravitational fields at well defined points in space. This concept makes the transition to a quantized gravitational theory harder because, in quantum mechanics, it´s impossible to work at a well defined point in space. Recent developments in black hole physics show us that this problem can be solved by incorporating the wave-particle duality into gravitational theory, resulting in a quantization of phase space. In this paper, we investigate a gravitational theory defined at the universe line of a massless relativistic particle. Using constrained Hamiltonian method, we are able of showing that the wave-particle duality relates the particle´s local symmetry and equations of motion in presence of position dependent tensorial fields with local symmetry and equations of motion in presence of momentum dependent tensorial fields. It reveals a dual gravitation of relativistic particles.