Valores fracos, variáveis modulares e o espaço de fase quântico

Abstract

This work intends to investigate the concepts of weak value and modular variables in quantum mechanics. To better understand the concept of weak value, we introduce the two state formalism of quantum mechanics and the von Neumann model for an ideal measurement, both of which derive the weak value. We present previous results in which we applied the coherent state method to describe the phase space in order to better analyze the effects in the measurement system when there is an interaction between it and the system being measured. We also present a critical analysis of the ideas introduced by Tamate in the investigation of the weak value, in which the geometrical aspects of the quantum state space were considered. We also propose a natural way to define the modular variables, that were introduced by Aharonov, Pendleton and Peterson in 1969, to describe non-local aspects that arise in some quantum phenomena, such as the Aharonov-Bohm effect. To do so,we use the description of the quantum state space of finite dimension constructed by Schwinger, as well as its limit to the continuous, and the results obtained by Lobo e Nemes, that says that a quantum physical system represented by a tensor product between two quantum spaces of states of finite and coprime dimensions, can not be considered as asystem composed by two degrees of freedom, but in fact, only one degree of freedom