Lorentz symmetry breaking as a quantum field theory regulator

Abstract

Perturbative expansions of relativistic quantum field theories typically contain ultraviolet divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. We shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory, and discuss its implications. We shall quantify just "how much" Lorentz symmetry breaking is required to fully regulate the theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [arXiv:0901.3775 [hep-th]] on 3+1 dimensional quantum gravity.

15 pages; 3 figures; V2: five references added, two minor typos fixed. no change in physics; V3: seven pages, zero figures, various references added and updated, discussion somewhat streamlined. no change in physics. This version accepted for publication in Physical Review D

References in corpus (5)

• Quantum Gravity at a Lifshitz Point
• Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope
• Renormalization of Lorentz violating theories
• Trans-Planckian physics and signature change events in Bose gas hydrodynamics
• Derivation of Lorentz Invariance and Three Space Dimensions in Generic Field Theory

Cited by in corpus (12)

• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Strong coupling in Horava gravity
• Cosmology of the Lifshitz universe
• Thermodynamics of Black Holes in Horava-Lifshitz Gravity
• Testing Hořava-Lifshitz gravity using thin accretion disk properties
• On IR solutions in Horava gravity theories
• Anisotropic Cosmology and (Super)Stiff Matter in Hořava's Gravity Theory
• Generalized uncertainty principle and Hořava-Lifshitz gravity
• $C{P}^{N-1}$ Models at a Lifshitz Point
• Analogue Models for Emergent Gravity
• A Note on Quasi-Riemannian Gravity with Higher Derivatives
• A note on particle kinematics in Horava-Lifshitz scenarios