Field theories with high derivatives

Abstract

The relativistic field theories of elementary particles are extended to cases where the field equations are derived from Lagrangians containing all derivatives of the field quantities. Expressions for the current, the energy-momentum tensor, the angular-momentum tensor, and the symmetrized energy-momentum tensor are given. When the field interacts with an electromagnetic field, we introduce a subtraction procedure, by which all the above expressions are made gauge-invariant. The Hamiltonian formulation of the equations of motion in a gauge-invariant form is also given.After considering the Lagrangian L as a scalar in a general relativity transformation and thus a function of g_μν and their derivatives, the functional derivative of with respect to g_μν (x) at a point where the space time is flat is worked out. It is shown that this differs from the symmetrized energy-momentum tensor given in the above sections by a term which vanishes when certain operators S_ij are antisymmetrical or when the Lagrangian contains the first derivatives of the field quantities only and whose divergence to either μ or ν vanishes.