Substituting fields within the action: Consistency issues and some applications

Journal Article · Wed Dec 15 00:00:00 EST 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3525242· OSTI ID:21501225

Pons, Josep M ^[1]

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1. Departament d'Estructura i Constituents de la Materia and Institut de Ciencies del Cosmos, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain)

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.

• OSTI ID: 21501225
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 12; Other Information: DOI: 10.1063/1.3525242; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DEGREES OF FREEDOM
ELEMENTARY PARTICLES
EQUATIONS OF MOTION
GAUGE INVARIANCE
LAGRANGIAN FIELD THEORY
LAGRANGIAN FUNCTION
SYMMETRY
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY