# New Energy-Momentum and Angular Momentum Tensors with Applications to Nucleon Structure

## TL;DR

This paper introduces new energy-momentum and angular momentum tensors derived from a second-derivative Lagrangian, motivated by quantum measurement considerations, offering fresh insights into nucleon structure analysis.

## Contribution

It proposes novel tensors that differ from traditional forms, derived via Noether's theorem from a second-derivative Lagrangian, with applications to nucleon structure.

## Key findings

- New tensors are proportional in mutual eigen-states.
- Traditional tensors are incompatible with the proposed criterion.
- Application to nucleon structure provides new theoretical perspectives.

## Abstract

We present a new type of energy-momentum tensor and angular momentum tensor. They are motivated by a special consideration in quantum measurement: Given a wave in mutual eigen-state of more than one physical observables, the corresponding physical currents should be proportional to each other. Interestingly, this criterion denies the traditional canonical and symmetric expressions of energy-momentum tensor and their associated expressions of angular momentum tensor. The new tensors we propose can be derived as Noether currents from a Lagrangian with second derivative, and shed new light on the study of nucleon structures.