Quadratic Actions in Dependent Fields and the Action Principle

General field theories are considered, within the functional differential formalism of quantum field theory, with interaction Lagrangian densities L I ( x ; λ ), with λ a generic coupling constant, such that the following expression ∂ L I ( x ; λ )/ ∂ λ may be expressed as quadratic functions in dep...

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Bibliographic Details
Published in:International journal of theoretical physics 2008-05, Vol.47 (5), p.1424-1431
Main Authors: Manoukian, E. B., Limboonsong, K.
Format: Article
Language:English
Subjects:
Elementary Particles
Gauge theory
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quadratic equations
Quantum Field Theory
Quantum Physics
Quantum theory
Theoretical
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Summary:General field theories are considered, within the functional differential formalism of quantum field theory, with interaction Lagrangian densities L I ( x ; λ ), with λ a generic coupling constant, such that the following expression ∂ L I ( x ; λ )/ ∂ λ may be expressed as quadratic functions in dependent fields but may, in general, be arbitrary functions of independent fields. These necessarily include, as special cases, present renormalizable gauge theories. It is shown, in a unified manner, that the vacuum-to-vacuum transition amplitude (the generating functional) may be explicitly derived in functional differential form which, in general, leads to modifications to computational rules by including such factors as Faddeev–Popov ones and modifications thereof which are explicitly obtained. The derivation is given in the presence of external sources and does not rely on any symmetry and invariance arguments as is often done in gauge theories and no appeal is made to path integrals.
ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-007-9584-y