Continuum Moment Equations on the Lattice

TL;DR

This paper investigates the challenges of evaluating continuum moment equations on the lattice, focusing on specific cases like nucleon magnetic moments and pseudoscalar charge radii, highlighting fundamental limitations.

Contribution

It provides a detailed analysis explaining why direct evaluation of continuum moment equations on the lattice is problematic, with case studies on nucleon properties.

Findings

Direct evaluation of continuum moments on the lattice is generally not feasible.

Analysis of three-point and four-point functions reveals fundamental limitations.

Highlights the need for alternative methods to compute continuum moments on the lattice.

Abstract

An analysis is given as to why one can not directly evaluate continuum moment equations, i.e., equations involving powers of the position variable times charge, current, or energy/momentum operators, on the lattice. I examine two cases: a three point function evaluation of the nucleon magnetic moment and a four point function (charge overlap) evaluation of the pseudoscalar charge radius.