Uncertainty Relations and Quantum Effects of Constraints in Chern-Simons Theory

TL;DR

This paper investigates quantum fluctuations in Abelian Chern-Simons theories caused by constraints, revealing how these fluctuations generate an effective mass in coupled scalar fields.

Contribution

It systematically derives quantum fluctuation terms in Abelian Chern-Simons theory using the projection operator method and dynamical constraints, linking them to mass generation.

Findings

Quantum fluctuations produce an effective mass in scalar fields.

Constraints induce quantum fluctuations via the uncertainty principle.

Methodology applies the projection operator approach to gauge theories.

Abstract

It is well known that Chern-Simons Theories are in the constrained systems and their total Hamiltonians become identically zero, because of their gauge invariance. While treating the constraints quantum mechanially, it will be expected taht there remain the quantum fluctuations due to the uncertainty principle. Using the projection operator method (POM) and the theory of dynamical constraints, such fluctuation terms are systematically derived in the case of Abelian Chern-Simons theory. It is shown that these terms produce the effective mass in the complex scalar fields coupled to the CS fields.