Quantum Measurements and the kappa--Poincare Group

TL;DR

This paper explores how the kappa--Poincare group, a symmetry related to quantum gravity, affects the path integral formulation of quantum mechanics, suggesting it could lead to decoherence and impact the understanding of quantum measurement.

Contribution

It analyzes the implications of kappa--Poincare symmetry on quantum path integrals, revealing potential loss of fundamental properties and connections to decoherence in quantum gravity.

Findings

Loss of time dependence in the evolution operator

Breakdown of composition law for successive events

Potential link between kappa--Poincare symmetry and decoherence

Abstract

The possible description of the vacuum of quantum gravity through the so called kappa--Poincare group is analyzed considering some of the consequences of this symmetry in the path integral formulation of nonrelativistic quantum theory. This study is carried out with two cases, firstly, a free particle, and finally, the situation of a particle immersed in a homogeneous gravitational field. It will be shown that the kappa--Poincare group implies the loss of some of the basic properties associated to Feynman's path integral. For instance, loss of the group characteristic related to the time dependence of the evolution operator, or the breakdown of the composition law for amplitudes of events occurring successively in time. Additionally some similarities between the present idea and the so called restricted path integral formalism will be underlined. These analogies advocate the claim that if the kappa--Poincare group contains some of the physical information of the quantum gravity vacuum, then this vacuum could entail decoherence. This last result will also allow us to consider the possibility of analyzing the continuous measurement problem of quantum theory from a group--theoretical point of view, but now taking into account the kappa--Poincare symmetries.