Tree-Level Unitarity and Renormalizability in Lifshitz Scalar Theory

TL;DR

This paper investigates unitarity and renormalizability in Lifshitz scalar theories, revealing that despite anisotropic scaling and broken Lorentz symmetry, the conditions align with those in relativistic theories, with modifications for power counting and frame dependence.

Contribution

It demonstrates that unitarity and renormalizability conditions in Lifshitz scalar theories are equivalent to those in relativistic theories, with necessary extensions for power counting and frame dependence.

Findings

Extended power counting condition is necessary for renormalizability.

Stronger unitarity constraints arise due to frame dependence.

Conditions match those of relativistic theories despite anisotropic scaling.

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.