Weighted Power Counting and Perturbative Unitarity

TL;DR

This paper explores the connection between renormalizability and unitarity at Lifshitz points, demonstrating their equivalence through tree unitarity tests in scalar, fermion, and gauge theories.

Contribution

It establishes that weighted power-counting renormalizability is equivalent to tree unitarity at Lifshitz points in various quantum field theories.

Findings

Weighted power-counting renormalizability equals tree unitarity.

Confirmed equivalence for scalar and fermion theories.

Confirmed equivalence for pure gauge theories.

Abstract

We consider the relationship between renormalizability and unitarity at a Lifshitz point in d dimensions. We test tree unitarity for theories containing only scalars and fermions, and for pure gauge theory. In both cases, we find the requirement of weighted power-counting renormalizability is equivalent to that of tree unitarity.