James M. Nester

Presymplectic manifolds and the Dirac–Bergmann theory of constraints

We present an algorithm which enables us to state necessary and sufficient conditions for the solvability of generalized Hamilton‐type equations of the form ι (X) ω=α on a presymplectic manifold (M,ω) where α is a closed 1‐form. The algorithm is phrased in the context of global infinite‐dimensional symplectic geometry, and generalizes as well as improves upon the local Dirac–Bergmann theory of constraints. The relation between our algorithm and the geometric constraint theory of Śniatycki, Tulczyjew, and Lichnerowicz is discussed.

The effect of gravitational interaction on classical fields: A hamilton-dirac analysis

Abstract We use the Hamilton-Dirac 3 + 1 analysis to clarify the effect of a dynamic gravitational interaction on “higher spin” or “derivative-coupled” fields. We find that when the non-gravitationally coupled version of a given field theory has constraints, the introduction of a gravitational interaction tends to destroy some of them, in a predictable way. The loss of these constraints leads to discontinuities in the number of degrees of freedom in such field theories when one passes from dynamic gravitational coupling to the special relativistic flat space limit. We also find, working from the 3 + 1 point of view, that the gravitationally coupled higher spin theories tend to have evolution singularities when certain of the field components pass through zero. Both the degrees of freedom discontinuities and the evolution singularties cause problems with the special relativistic correspondence principle limit for the higher spin fields with constraints.

Extension of the York field decomposition to general gravitationally coupled fields

Abstract We extend the York decomposition analysis of the initial value constraints to general gravitationally coupled classical field theories. The decomposition is found to be particularly useful in solving the constraint equations for all theories of current physical interest. These include Einstein gravity or Einstein-Cartan (torsion) gravity coupled to the massive or massless version of the following: general scalar (including Klein-Gordon, Brans-Dicke, and Higgs), Dirac spin 1/2, Maxwell (Proca) and Yang-Mills (any gauge group). We show in detail how the program works for the general Yang-Mills field and for the Einstein-Cartan-Proca field.