Induced quantum numbers of a magnetic monopole at finite temperature

TL;DR

This paper investigates how a magnetic monopole influences quantum numbers like charge and angular momentum in a Dirac electron system at finite temperature, revealing conditions for sharp quantum observables.

Contribution

It introduces a detailed analysis of temperature-dependent induced quantum numbers and fluctuations in a Dirac monopole system, including the effects of CP violation.

Findings

Electric charge and angular momentum are induced by the monopole.

Temperature affects the functional dependence of induced quantum numbers.

Conditions are identified when charge and angular momentum become sharp quantum observables.

Abstract

A Dirac electron field is quantized in the background of a Dirac magnetic monopole, and the phenomenon of induced quantum numbers in this system is analyzed. We show that, in addition to electric charge, also squares of orbital angular momentum, spin, and total angular momentum are induced. The functional dependence of these quantities on the temperature and the CP-violating vacuum angle is determined. Thermal quadratic fluctuations of charge and squared total angular momentum, as well as the correlation between them and their correlations with squared orbital angular momentum and squared spin, are examined. We find the conditions when charge and squared total angular momentum at zero temperature are sharp quantum observables rather than mere quantum averages.