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

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.

arXiv commentv3: This version match with the published paper

References in corpus (14)

• Quantum Gravity at a Lifshitz Point
• The Dynamics of General Relativity
• Membranes at Quantum Criticality
• A healthy extension of Horava gravity
• Renormalization of Horava Gravity
• A Striking Property of the Gravitational Hamiltonian
• Hamiltonian structure of Horava gravity
• Hořava gravity is asymptotically free (in 2+1 dimensions)
• Lower-dimensional Horava-Lifshitz gravity
• Consistent Horava gravity without extra modes and equivalent to general relativity at the linearized level
• Quantization of Horava Gravity in 2+1 Dimensions
• Quantization of the Horava theory at the kinetic-conformal point
• The point-particle solution and the asymptotic flatness in 2+1 Horava gravity
• Dynamics of the anisotropic conformal Horava theory versus its kinetic-conformal formulation

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• Quantum Lagrangian of the Horava theory and its nonlocalities
• Effective action of the Horava theory: Cancellation of divergences
• Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory
• Quantizing non-projectable Hořava gravity with Lagrangian path integral
• Batalin-Fradkin-Vilkovisky Quantization of Quadratic Gravity
• Quantization of the anisotropic conformal Horava theory
• Curvature vs degrees of freedom: The case of the critical 2+1 Horava theory