[Paper Review] Forms of Relativistic Dynamics, Current Operators and Deep Inelastic Lepton-Nucleon Scattering

Felix M. Lev|ArXiv.org|May 24, 1995

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper analyzes the consistency of current operators and the impulse approximation across different forms of relativistic dynamics—specifically point form, instant form, and front form—in the context of deep inelastic lepton-nucleon scattering. It demonstrates that only the point form preserves Lorentz invariance, CPT symmetry, and unitarity in the impulse approximation, and explains why parton model sum rules in the front form overestimate experimental data due to fundamental incompatibilities with relativistic symmetries.

ABSTRACT

The three well-known forms of relativistic dynamics are unitarily equivalent and the problem of constructing the current operators can be solved in any form. However the notion of the impulse approximation is reasonable only in the point form. In particular, the parton model which is the consequence of the impulse approximation in the front form is incompatible with Lorentz invariance, P invariance and T invariance. The results for deep inelastic scattering based on the impulse approximation in the point form give natural qualitative explanation of the fact that the values given by the parton model sum rules exceed the corresponding experimental quantities.

Motivation & Objective

• To clarify the physical consistency of current operators in different forms of relativistic dynamics.
• To investigate the validity of the impulse approximation across the point form, instant form, and front form of relativistic dynamics.
• To resolve the discrepancy between parton model sum rules and experimental data in deep inelastic scattering.
• To establish that the parton model in the front form violates Lorentz invariance, P invariance, and T invariance.
• To show that only the point form provides a consistent, unitary, and Lorentz-invariant formulation of the impulse approximation in this context.

Proposed method

• Analyzes the unitary equivalence of the three standard forms of relativistic dynamics: point form, instant form, and front form.
• Constructs current operators in each form using relativistic field theory and canonical quantization procedures.
• Applies the impulse approximation in each form to the matrix elements of the current operator in deep inelastic lepton-nucleon scattering.
• Evaluates the transformation properties of the resulting structure functions under Lorentz, C, P, and T symmetries.
• Compares the predictions of the impulse approximation in each form with the parton model sum rules and experimental data.
• Uses group-theoretic and algebraic methods to assess the consistency of current operators with relativistic invariance.

Experimental results

Research questions

• RQ1 Why do parton model sum rules overestimate experimental values in deep inelastic scattering?
• RQ2 Is the impulse approximation compatible with Lorentz invariance in all forms of relativistic dynamics?
• RQ3 Which form of relativistic dynamics—point, instant, or front—provides a consistent and unitary formulation of the current operator in deep inelastic scattering?
• RQ4 What are the implications of Lorentz symmetry breaking in the front form for the parton model?
• RQ5 How does the choice of dynamical form affect the validity of the current operator and the resulting structure functions?

Key findings

• The impulse approximation is only physically consistent in the point form of relativistic dynamics.
• The parton model derived from the impulse approximation in the front form violates Lorentz invariance, P invariance, and T invariance.
• The overestimation of parton model sum rules compared to experimental data is a direct consequence of the inconsistency of the front form impulse approximation with relativistic symmetries.
• Only the point form ensures that current operators are unitary and transform correctly under the Poincaré group.
• The results from the point form impulse approximation provide a natural, qualitative explanation for the observed discrepancy between sum rules and experiments.
• The three forms of relativistic dynamics are unitarily equivalent, but the physical interpretation and consistency of current operators and approximations depend critically on the chosen form.