Tree-Level Unitarity and Renormalizability in Lifshitz Scalar Theory

Abstract

We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability conditions are modified from those in relativistic theories. We show that for renormalizability, an extended version of the power counting condition is required in addition to the conventional one. The unitarity bound for S-matrix elements also gives stronger constraints on interaction terms because of the reference frame dependence of scattering amplitudes. We prove that both unitarity and renormalizability require identical conditions as in the case of conventional relativistic theories.

31 pages, 11 figures

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• Horava-Lifshitz Cosmology: A Review
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• Stable Singularity-free Cosmological Solutions in non-projectable Horava-Lifshitz Gravity
• S-matrix Unitarity and Renormalizability in Higher Derivative Theories
• Matter scattering in $R_{\mu \nu }^2$ gravity and unitarity
• Thermodynamics and and phase transition of topological dilatonic Lifshitz-like black holes
• High-energy properties of the graviton scattering in quadratic gravity
• Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time
• Barboza-Alcaniz Equation of State Parametrization : Constraining the Parameters in Different Gravity Theories
• Universal horizons and Hawking radiation in nonprojectable 2d Hořava gravity coupled with a non-relativistic scalar field