Lorentz invariance in heavy particle effective theories

TL;DR

This paper develops a formalism using Lorentz group representations to construct heavy particle effective Lagrangians, clarifies the link between Lorentz and reparameterization invariance, and discusses extensions to various field types.

Contribution

It introduces a new formalism based on induced Lorentz representations for heavy particle effective theories and analyzes invariance constraints and their limitations.

Findings

Derived Lagrangian constraints for Lorentz invariance of the S matrix.

Identified breakdown of standard reparameterization invariance at order 1/M^4.

Extended formalism to arbitrary spin and self-conjugate fields.

Abstract

Employing induced representations of the Lorentz group (Wigner's little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the S matrix are derived. The relationship between Lorentz invariance and reparameterization invariance is established and it is shown why a standard ansatz for implementing reparameterization invariance in heavy fermion effective Lagrangians breaks down at order 1/M^4. Formalism for fields of arbitrary spin and for self-conjugate fields is presented, and the extension to effective theories of massless fields is discussed.