Abstract
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.
Highlights
Horava theory [1,2] is a geometrical field theory that may be used to study quantum gravity since it is power-counting renormalizable and unitary
We focus on the path integral quantization, since it is more adaptable to a gravitational field theory as the Horava theory
We consider in the Lagrangian all the inequivalent terms that are compatible with the foliation-preserving diffeomorphisms (FDiff) symmetry, up to the minimal order in spatial derivatives required by power-counting renormalizability, which is z 1⁄4 2 in the 2 þ 1 theory [1]
Summary
Horava theory [1,2] is a geometrical field theory that may be used to study quantum gravity since it is power-counting renormalizable and unitary. In the case of the nonprojectable 3 þ 1 Horava gravity, the Lagrangian includes a number of the order of 102 different terms that are compatible with the FDiff gauge symmetry. An essential feature of the nonprojectable theory is the presence of second-class constraints This fact forces us to consider the quantization in rather different approaches to ones used in general relativity, projectable Horava theory, and gauge theories in general with only first-class constraints. We consider in the Lagrangian all the inequivalent terms that are compatible with the FDiff symmetry, up to the minimal order in spatial derivatives required by power-counting renormalizability, which is z 1⁄4 2 in the 2 þ 1 theory [1]. More consequences on the value of the energy and the role of the higher order terms were considered in that reference
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.