An extension of the Faddeev–Jackiw technique to fields in curved spacetimes

Academic Article


  • The Legendre transformation on singular Lagrangians, e.g. Lagrangians representing gauge theories, fails due to the presence of constraints. The Faddeev-Jackiw technique, which offers an alternative to that of Dirac, is a symplectic approach to calculating a Hamiltonian paired with a well-defined initial value problem when working with a singular Lagrangian. This phase space coordinate reduction was generalized by Barcelos-Neto and Wotzasek to simplify its application. We present an extension of the Faddeev-Jackiw technique for constraint reduction in gauge field theories and non-gauge field theories that are coupled to a curved spacetime that is described by General Relativity. A major difference from previous formulations is that we do not explicitly construct the symplectic matrix, as that is not necessary. We find that the technique is a useful tool that avoids some of the subtle complications of the Dirac approach to constraints. We apply this formulation to the Ginzburg-Landau action and provide a calculation of its Hamiltonian and Poisson brackets in a curved spacetime.
  • Authors

  • Prescod-Weinstein, Chanda
  • Bertschinger, Edmund
  • Status

    Publication Date

  • April 9, 2015
  • Published In


  • gr-qc
  • hep-th
  • Digital Object Identifier (doi)

    Start Page

  • 075011
  • End Page

  • 075011
  • Volume

  • 32
  • Issue

  • 7