Quantum Lagrangian of the Horava theory and its nonlocalities

Abstract

We perform the BFV quantization of the 2+1 projectable and the 3+1 nonprojectable versions of the Horava theory. This is a Hamiltonian formalism, and noncanonical gauges can be used with it. In the projectable case, we show that the integration on canonical momenta reproduces the quantum Lagrangian known from the proof of renormalization of Barvinsky et al. This quantum Lagrangian is nonlocal, its nonlocality originally arose as a consequence of getting regular propagators. The matching of the BFV quantization with the quantum Lagrangian reinforces the program of quantization of the Horava theory. We introduce a local gauge-fixing condition, hence a local Hamiltonian, that leads to the nonlocality of the Lagrangian after the integration. For the case of the nonprojectable theory, this procedure allows us to obtain the complete (nonlocal) quantum Lagrangian that takes into account the second-class contraints. We compare with the integration in general relativity, making clear the relationship between the underlying anisotropic symmetry of the Horava theory and the nonlocality of its quantum Lagrangian.

arXiv commentv2: Minor change in title, other minor corrections on wording

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Cited by in corpus (6)

• Cancellation of divergences in the nonprojectable Horava theory
• BRST symmetry and unitarity of the Horava theory
• Renormalization of the nonprojectable Horava theory
• Effective action of the Horava theory: Cancellation of divergences
• Batalin-Fradkin-Vilkovisky Quantization of Quadratic Gravity
• Quantization of the anisotropic conformal Horava theory