On the quantization of field theories derived from higher order lagrangians

Abstract

Heisenberg and Pauli ( 1 ) have shown how to quantize field theories derived from a Lagrangian containing first derivatives of the field quantities only. The present paper extends the theory of quantization of fields to the case of higher order Lagrangians, i.e. Lagrangians in which higher derivatives than the first appear. It is shown how such field equations can be put into Hamiltonian form and how the quantization can subsequently be carried out. Both the cases of Einstein-Bose and Fermi-Dirac quantization are discussed. It is established that the quantization is relativistically invariant and consistent with the field equations. An interesting feature of the present theory is that the Hamiltonian proves to be different, in general, from the integral of the 4–4 component of the energy momentum tensor.