The Hamilton–Jacobi characteristic equations for three-dimensional Ashtekar gravity

Abstract

The Hamilton-Jacobi analysis of three dimensional gravity defined in terms of Ashtekar-like variables is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the gauge transformations of the theory are found. We find from integrability conditions on the Hamilton-Jacobi Hamiltonians that the theory is reduced to a BF field theory defined only in terms of self-dual (or anti-self-dual) variables; we identify the dynamical variables and the counting of physical degrees of freedom is performed. In addition, we compare our results with those reported by using the canonical formalism. PACS numbers: 98.80.-k,98.80.Cq * Electronic address: aescalan@ifuap.buap.mx † Electronic address:

The Hamilton-Jacobi analysis for higher order Maxwell-Chern-Simons gauge theory

“…we can observe that the theory is now linear in the temporal derivatives and we can apply the HJ analysis. From the definition of the momenta (π ν , πν , p ν ), canonically conjugated to (ξ µ , v µ , ψ µ ) respectively, we find the following Hamiltonians [12][13][14][15][16][17][18]]…”

“…where σ 1 , σ 2 , σ 3 are parameters associated to the Hamiltonians. Now we calculate the characteristic equations from the fundamental differential, which will reveal the symmetries of the theory [12][13][14][15][16][17][18].…”

“…Using this approach, the construction of the fundamental differential is straightforward and and the identification of symmetries is, in general, more economical than other approaches [12][13][14][15][16][17][18].…”

The Hamilton-Jacobi analysis for higher-order Chern-Simons gravity

“…) are the canonical variables and P µ = (π 00 , π 0i , π ij , π00 , π0i , πij , p 00 , p 0i , p ij ) their corresponding momenta, we find the following Hamiltonians [17][18][19][20][21][22][23][24][25] Ω 00 = π 00 + ψ 00 = 0,…”

“…The noninvolutives are removed through the introduction of the generalized HJ brackets. From the fundamental differential we can obatain the characteristic equations, the gauge symmetries, and the identification of symmetries is more economical than OD [22][23][24][25].…”