Substituting fields within the action: consistency issues and some applications

摘要

In field theory, as well as in mechanics, the substitution of some fields interms of other fields at the level of the action raises an issue of consistencywith respect to the equations of motion. We discuss this issue and give anexpression which neatly displays the difference between doing the substitutionat the level of the Lagrangian or at the level of the equations of motion. Bothoperations do not commute in general. A very relevant exception is the case ofauxiliary variables, which are discussed in detail together with some of theirrelevant applications. We discuss the conditions for the preservation ofsymmetries - Noether as well as non-Noether - under the reduction of degrees offreedom provided by the mechanism of substitution. We also examine how thegauge fixing procedures fit in our framework and give simple examples on theissue of consistency in this case.