Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-03-15
Theor.Math.Phys. 123 (2000) 683-700; Teor.Mat.Fiz. 123 (2000) 323-344
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 21 pages, M.V. Saveliev's memorial volume of Theor. Math. Phys
Scientific paper
We formulate the equations of motion of a free scalar field in the flat and $AdS$ space of an arbitrary dimension in the form of some "higher spin" covariant constancy conditions. Klein-Gordon equation is interpreted as a non-trivial cohomology of a certain "\sgm-complex". The action principle for a scalar field is formulated in terms of the "higher-spin" covariant derivatives for an arbitrary mass in $AdS_d$ and for a non-zero mass in the flat space. The constructed action is shown to be equivalent to the standard first-order Klein-Gordon action at the quadratic level but becomes different at the interaction level because of the presence of an infinite set of auxiliary fields which do not contribute at the free level. The example of Yang-Mills current interaction is considered in some detail. It is shown in particular how the proposed action generates the pseudolocally exact form of the matter currents in $AdS_d$.
Shaynkman O. V.
Vasiliev Mikhail A.
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