The canonical formulation of E6(6) exceptional field theory

We investigate the canonical formulation of the (bosonic) E6(6) exceptional field theory. The explicit non-integral (not manifestly gauge invariant) topological term of E6(6) exceptional field theory is constructed and we consider the canonical formulation of a model theory based on the topological two-form kinetic term. Furthermore we construct the canonical momenta and the canonical Hamiltonian of the full bosonic E6(6) exceptional field theory. Most of the canonical gauge transformations and some parts of the canonical constraint algebra are calculated. Moreover we discuss how to translate the results canonically into the generalised vielbein formulation. We comment on the possible existence of generalised Ashtekar variables.

Abelian Ashtekar formulation from the ADM action

We study the Ashtekar formulation of linear gravity starting from the Arnowitt–Deser–Misner (ADM) first-order action of the exact theory, linearizing it, and performing a canonical transformation that coordinatizes the phase-space in terms of the already linearized Ashtekar variables. A quantum geometrical representation, based on the realization of the transverse-traceless part of the linear canonical variables, is presented, and its relationship with previous attempts is discussed. A related geometric representation that realizes directly the observables of the Fierz–Pauli theory, without resorting to deal with the linearized Ashtekar variables, is also discussed.