arXiv subjects

J. Manuel-Cabrera

Publications and source records attributed to J. Manuel-Cabrera.

3 recordsLinked to original sources

arXiv2026

Gauge-Unfixed Hamiltonian Casimir and Static Torsionful Sector in the Katanaev-Volovich Model

Hamiltonian analysis of the first-order Katanaev-Volovich model of two-dimensional gravity with torsion. The first-order action already singles out natural canonical pairs: the auxiliary Lorentz scalars are conjugate to the spatial connection and zweibein. An extended Dirac-Bergmann embedding isolates an auxiliary second-class sector whose elimination recovers the canonical structure encoded in the first-order action and leaves the first-class constraints generating the local gauge symmetries. An independent Faddeev-Jackiw reduction yields the same reduced brackets. The Katanaev/Poisson-Sigma Casimir is then recovered, up to normalization, directly from the reduced Dirac-Bergmann first-class constraint ideal, before imposing any gauge condition. This identifies the Casimir as a global label of the reduced canonical sectors; after the static normalization is chosen, it supplies the Hamiltonian parameter of the torsionful branch. The same normalization is applied to that branch in dilaton gauge, whose field equations are verified on shell. In this static sector the Casimir-normalized radial field does not coincide with the metric Killing norm: the diagonal representative satisfies \(NB=e^{4\beta r}\). Consequently, torsion modifies the Killing temperature through the normalization of the Killing time, while the horizon entropy retains its standard two-dimensional dilaton value and the Casimir-normalized first law holds.

gr-qc↗

arXiv2015

Faddeev-Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

A detailed Faddeev-Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev-Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev-Jackiw brackets and Dirac's brackets coincide to each other. Finally we discuss some remarks and prospects.

math-ph↗

arXiv2014

Hamiltonian dynamics of an exotic action for gravity in three dimensions

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.

hep-th↗