arXiv subjects

Byron Droguett

Publications and source records attributed to Byron Droguett.

23 records · Page 2Linked to original sources

arXiv2021

BFV quantization of the nonprojectable 2+1 Horava theory

We show that the BFV quantization scheme can be implemented in the nonprojectable 2+1 Horava theory. This opens the possibility of imposing more general gauge conditions in the quantization of this theory. The BFV quantization is based on the canonical formalism, which is suitable to incorporate the measure associated to the second-class constraints that the theory has. Special features of the Hamiltonian density and the matrix of second-class constraints allow that the system be involutive in terms of Dirac brackets, which is a nontrivial requisite for implementing the BFV formalism. We present the BRST symmetry transformations in the canonical variables. The theory is of rank one, in the classification introduced by Fradkin and Fradkina. The originally called relativistic gauge-fixing conditions of the BFV formalism can be implemented in the nonprojectable Horava theory, extended to nonrelativistic forms. We show that the nonlocal gauge condition introduced in the projectable theory can be included among these gauges.

hep-th↗

arXiv2020

Curvature vs degrees of freedom: The case of the critical 2+1 Horava theory

We present the interesting case of the 2+1 nonprojectable Horava theory formulated at the critical point, where it does not posses local degrees of freedom. The critical point is defined by the value of a coupling constant of the theory. We discuss how, in spite of the absence of degrees of freedom, the theory admits solutions with nonflat or nonconstant curvature. We consider the theory without cosmological constant and without terms of higher order derivatives, hence this is an effect that can be seen at the same order of 2+1 general relativity. We present an exact nonflat solution that is not asymptotically flat. The presence of solutions with nontrivial curvature seems to be related to the relaxing of the asymptotically flat condition. We discuss that there is no analogue of Newtonian potential in this theory, and a broad class of asymptotically flat geometries leads to the restriction that the only solutions that can be found among them are the flat ones.

gr-qc↗

arXiv2020

The point-particle solution and the asymptotic flatness in 2+1 Horava gravity

We show that the solution corresponding to the gravitational field of a point particle at rest in 2+1 nonprojectable Horava is exactly the same as its analogous in 2+1 General Relativity. This solution is well known, it is a flat cone whose deficit angle is proportional to the mass of the particle. To establish the system we couple the Horava theory to a point particle with relativistic action. As a consequence of this result, we define the condition of asymptotic flatness exactly in the same way of 2+1 General Relativity. A remarkable feature of this condition is that the dominant mode is not fixed, but affected by the mass of the configuration. Anoter important coincidence with 2+1 General Relativity under asymptotic flatness is that the energy is the same (except for some coupling constants involved), the z = 1 term with the derivative of the lapse function does not contribute.

gr-qc↗

arXiv2020

Dynamics of the anisotropic conformal Horava theory versus its kinetic-conformal formulation

We contrast the dynamics of the Horava theory with anisotropic Weyl symmetry with the case when this symmetry is explicitly broken, which is called the kinetic-conformal Horava theory. To do so we perform the canonical formulation of the anisotropic conformal theory at the classical level with a general conformal potential. Both theories have the generator of the anisotropic Weyl transformations as a constraint but it changes from first to second-class when the Weyl symmetry is broken. The FDiff-covariant vector a_i = \partial_i \ln N plays the role of gauge connection for the anisotropic Weyl transformations. A Lagrange multiplier plays also the role of gauge connection, being the time component. The anisotropic conformal theory propagates the same number of degrees of freedom of the kinetic-conformal theory, which in turn are the same of General Relativity. This is due to exchange of a second-class constraint in the kinetic-conformal case by a gauge symmetry in the anisotropic conformal case. An exception occurs if the conformal potential does not depend on the lapse function N, as is the case of the so called Cotton^2 potential, in which case one of the physical modes becomes odd. We develop in detail two explicit anisotropic conformal models. One of them depends on N whereas the other one is the Cotton^2 model. We also study conformally flat solutions in the anisotropic conformal and the kinetic-conformal theories, defining as conformally flat the spatial metric, but leaving for N a form different to the one dictated by the anisotropic Weyl transformations. We find that in both theories these configurations have vanishing canonical momentum and they are critical points of the potential. In the kinetic-conformal theory we find explicitly an exact, nontrivial, conformally flat solution.

hep-th↗

arXiv2020

Quantization of the nonprojectable 2+1D Horava theory: The second-class constraints

We present the quantization of the 2+1 dimensional nonprojectable Horava theory. The central point of the approach is that this is a theory with second-class constraints, hence the quantization procedure must take account of them. We consider all the terms in the Lagrangian that are compatible with the foliation-preserving-diffeomorphisms symmetry, up to the z=2 order which is the minimal order indicated by power-counting renormalizability. The measure of the path integral must be adapted to the second-class constraints, and this has consequences in the quantum dynamics of the theory. Since this measure is defined in terms of Poisson brackets between the second-class constraints, we develop all the Hamiltonian formulation of the theory with the full Lagrangian. We found that the propagator of the lapse function (and the one of the metric) acquires a totally regular form. The quantization requires the incorporation of a Lagrange multiplier for a second-class constraint and fermionic ghosts associated to the measure of the second-class constraints. These auxiliary variables have still nonregular propagators.

hep-th↗