Quantization of nonlocal fractional field theories via the extension problem

Abstract

We use the extension problem proposed by Caffarelli and Silvestre to study the quantization of a scalar nonlocal quantum field theory built out of the fractional Laplacian. We show that the quantum behavior of such a nonlocal field theory in $d$-dimensions can be described in terms of a local action in $d+1$ dimensions which can be quantized using the canonical operator formalism though giving up local commutativity. In particular, we discuss how to obtain the two-point correlation functions and the vacuum energy density of the nonlocal fractional theory as a brane limit of the bulk correlators. We show explicitly how the quantized extension problem reproduces exactly the same particle content of other approaches based on the spectral representation of the fractional propagator. We also briefly discuss the inverse fractional Laplacian and possible applications of this approach in general relativity and cosmology.

arXiv comment28 pages, no figures

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• On the Kuzmin model in fractional Newtonian gravity
• Quantum scalar field theories with fractional operators
• Casimir-Polder interactions with massive photons: implications for BSM physics
• Representations of the fractional d'Alembertian and initial conditions in fractional dynamics
• Aspects of entanglement in non-local field theories with fractional Laplacian
• Horizon Fractalization in Black Strings Ungravity
• Fractional Particle and Sigma Model
• Constructing a weakly-interacting fixed point of the Fermionic Polchinski equation
• Cosmology of fractional gravity