34 research outputs found
Closure of the algebra of constraints for a nonprojectable Ho\v{r}ava model
We perform the Hamiltonian analysis for a nonprojectable Horava model whose
potential is composed of R and R^2 terms. We show that Dirac's algorithm for
the preservation of the constraints can be done in a closed way, hence the
algebra of constraints for this model is consistent. The model has an extra,
odd, scalar mode whose decoupling limit can be seen in a linear-order
perturbative analysis on weakly varying backgrounds.
Although our results for this model point in favor of the consistency of the
Ho\v{r}ava theory, the validity of the full nonprojectable theory still remains
unanswered.Comment: Some comments added in conclusions and abstract. Version published in
Phys. Rev. D. 15 pages, 1 figur
Singular Lagrangians and Its Corresponding Hamiltonian Structures
We present a general procedure to obtain the Lagrangian and associated Hamiltonian structure for integrable systems of the Helmholtz type. We present the analysis for coupled Kortewegâde Vries systems that are extensions of the Kortewegâde Vries equation. Starting with the system of partial differential equations it is possible to follow the Helmholtz approach to construct one or more Lagrangians whose stationary points coincide with the original system. All the Lagrangians are singular. Following the Dirac approach, we obtain all the constraints of the formulation and construct the Poisson bracket on the physical phase space via the Dirac bracket. We show compatibility of some of these Poisson structures. We obtain the Gardner Δâdeformation of these systems and construct a master Lagrangian which describe the coupled systems in the weak Δâlimit and its modified version in the strong Δâlimit
Quantum aspects of the gravitational-gauge vector coupling in the Ho\v{r}ava-Lifshitz theory at the kinetic conformal point
This work presents the main aspects of the anisotropic gravity-vector gauge
coupling at all energy scales \i.e., from the IR to the UV point. This study is
carry out starting from the 4+1 dimensional Ho\v{r}ava-Lifshitz theory, at the
kinetic conformal point.The Kaluza-Klein technology is employed as a unifying
mechanism to couple both interactions. Furthermore, by assuming the so-called
cylindrical condition, the dimensional reduction to 3+1 dimensions leads to a
theory whose underlying group of symmetries corresponds to the diffeomorphisms
preserving the foliation of the manifold and a U(1) gauge symmetry. The
counting of the degrees of freedom shows that the theory propagates the same
spectrum of Einstein-Maxwell theory. The speed of propagation of tensorial and
gauge modes is the same, in agreement with recent observations. This point is
thoroughly studied taking into account all the terms that
contribute to the action. In contrast with the 3+1 dimensional formulation,
here the Weyl tensor contributes in a non-trivial way to the potential of the
theory. Its complete contribution to the 3+1 theory is explicitly obtained.
Additionally, it is shown that the constraints and equations determining the
full set of Lagrange multipliers are elliptic partial differential equations of
eighth-order. To check and assure the consistency and positivity of the reduced
Hamiltonian some restrictions are imposed on the coupling constants. The
propagator of the gravitational and gauge sectors are obtained showing that
there are not ghost fields, what is more they exhibit the scaling for all
physical modes at the high energy level. By evaluating the superficial degree
of divergence and considering the structure of the second class constraints, it
is shown that the theory is power-counting renormalizable