Method of Construction of Gauge-Invariant Lagrangians for Arbitrary Lie Groups

The general method of construction of gauge-invariant Lagrangians that is based on the fibre bundle theory and group transformations, is proposed. The method enables one to obtain Lagrangians with the exact and spontaneously broken symmetry. To illustrate, the Lagrangian of the inhomogeneous gauge group £3= 0(3) x) T3 is constructed. The possibility of constructing a gauge-invariant action for the Poincare group, which satisfies physical requirements is analyzed. It is shown that the action cannot be obtained for the exact symmetry and it can be constructed for the spontaneously broken symmetry. In the latter case the action corresponds to the generalized gravitation theory containing, as a particular case, Einstein's relativity and also the theorieacinvolving torsion and squared curvature. Moreover, it becomes possible that the massive vector particles corresponding to the gauge fields of the translation subgroup would exist.