Hamiltonian dynamics of an exotic action for gravity in three dimensions

Abstract

The Hamiltonian dynamics and the canonical covariant formalism for an exotic action in three dimensions are performed. By working with the complete phase space, we report a complete Hamiltonian description of the theory such as the extended action, the extended Hamiltonian, the algebra among the constraints, the Dirac's brackets and the correct gauge transformations. In addition, we show that in spite of exotic action and tetrad gravity with a cosmological constant give rise to the same equations of motion, they are not equivalent, in fact, we show that their corresponding Dirac's brackets are quite different. Finally, we construct a gauge invariant symplectic form which in turn represents a complete Hamiltonian description of the covariant phase space.PACS numbers: 98.80.-k,98.80.Cq

Hamiltonian dynamics and gauge symmetry for three-dimensional Palatini theory with cosmological constant

“…This fact shows a difference among the so-called exotic action for gravity [8,28,29] and Palatini's theory. In fact, in [29] a detailed canonical analysis of exotic gravity is performed, and the following results are reported; there is not any restriction about the internal group, the gauge symmetry is an Λ-deformed Poincaré symmetry. However, the Dirac brackets among the dynamical variables are noncommutative and the cosmological constant can not vanish.…”

“…In this manner, we observe a difference at classical level among exotic action for gravity and Palatini's theory (see [29]). In fact, the Dirac brackets (2.27) are commutative and are different from (3.1); in (3.1) we can not take Λ = 0.…”

“…However, the Dirac brackets among the dynamical variables are noncommutative and the cosmological constant can not vanish. In fact, the Dirac brackets for exotic action are given by [29] …”

Hamiltonian dynamics and Faddeev–Jackiw formulation of 3D gravity with a Barbero–Immirzi like parameter

“…It is important to remark that if some of the Dirac steps is omitted, then it is possible to obtain incomplete results [11,12]. In this manner, an analysis developed on the full phase space and following all the Dirac steps is mandatory.…”

Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension

“…Our analysis will be carry out by performing a pure Dirac's method [14][15][16][17]; we develop a full constraints program and we construct the …”