TECHNIQUES OF HIGHER ORDER OSCULATOR BUNDLE
IN GENERALIZED GAUGE THEORY

Gheorghe Munteanu

1991 Math. Subject Classification: 53C80.

Abstract: Given a certain state of a mechanical system, the object of many
physical theories is to determine the way in which that  state  changes
in  time.  The  evolution  of  the  system  is  usually  gouverned   by
Euler-Lagrange equations and this evolution must look the same in every
coordinate system. In gauge theories, in  addition  to  the  invariance
under changes of coordinates, is involved another invariance, under the
so called gauge transformations. In classical gauge theory the physical
system is represented by  sections  in  an  associate  bundle,  and  is
required to be invariant with respect to this gauge change.

In  this  paper  we  shall  generalize  the   concept   of   gauge
transformation  of  one  system  developed  in a $k$-osculator   bundle
([7],[8]),  the  associate  bundle  of  the  bundle  of $k$-frames.  The
geometrical notion of gauge derivatives  is  studied  and  the $k$-order
Einstein Yang-Mills equations are obtained. A general  class  of  gauge
invariant Lagrangians is given.