Perfect and Imperfect Gauge Fixing

摘要

Gauge fixing may be done in different ways. We show that using the chainstructure to describe a constrained system, enables us to use either a perfectgauge, in which all gauged degrees of freedom are determined; or an imperfectgauge, in which some first class constraints remain as subsidiary conditions tobe imposed on the solutions of the equations of motion. We also show that thenumber of constants of motion depends on the level in a constraint chain inwhich the gauge fixing condition is imposed. The relativistic point particle,electromagnetism and the Polyakov string are discussed as examples and perfector imperfect gauges are distinguished.