An extension of the Faddeev–Jackiw technique to fields in curved spacetimes
Author(s)Bertschinger, Edmund; Prescod-Weinstein, Chanda
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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.
DepartmentKavli Institute for Astrophysics and Space Research; Massachusetts Institute of Technology. Department of Physics
Classical and Quantum Gravity
Prescod-Weinstein, C., and Edmund Bertschinger. “An Extension of the Faddeev–Jackiw Technique to Fields in Curved Spacetimes.” Classical and Quantum Gravity 32, no. 7 (March 17, 2015): 075011.
Author's final manuscript