Substituting fields within the action: Consistency issues and some applications

In field theory, as well as in mechanics, the substitution of some fields in terms of other fields at the level of the action raises an issue of consistency with respect to the equations of motion. We discuss this issue and give an expression which neatly displays the difference between doing the substitution at the level of the Lagrangian or at the level of the equations of motion. Both operations do not commute in general. A very relevant exception is the case of auxiliary variables, which are discussed in detail together with some of their relevant applications. We discuss the conditions for the preservation of symmetries-Noether as well as non-Noether-under the reduction of degrees of freedom provided by the mechanism of substitution. We also examine how the gauge fixing procedures fit in our framework and give simple examples on the issue of consistency in this case. (C) 2010 American Institute of Physics. [doi:10.1063/1.3525242]