[Paper Review] A retrospective look at Regge poles

Alessandro Bottino|arXiv (Cornell University)|Jul 6, 2018

Geometric Analysis and Curvature Flows5 references3 citations

TL;DR

This retrospective paper by Alessandro Bottino reviews Tullio Regge's foundational work on Regge poles, analyzing how complex energy and angular momentum properties of scattering amplitudes advanced S-matrix theory in the 1950s–60s. It highlights Regge's analytical approach as a pivotal framework for understanding strong interactions, with lasting influence on modern high-energy physics and quantum field theory.

ABSTRACT

The theoretical motivations that led Tullio Regge to investigate the analytical properties of the scattering amplitude of the collision process between two particles in terms of complex energy and complex angular momentum are briefly reviewed and set in the context of the S-matrix theory that was developed in the late Fifties and early Sixties of the last century, in an attempt to unravel the properties of the strong interaction.

Motivation & Objective

• To examine the theoretical motivations behind Tullio Regge's exploration of scattering amplitudes in complex energy and angular momentum planes.
• To contextualize Regge's work within the broader development of S-matrix theory during the late 1950s and early 1960s.
• To assess the historical significance and long-term influence of Regge poles on high-energy physics and quantum field theory.
• To document the intellectual trajectory of Regge's contributions in the context of the scientific community's evolving understanding of strong interactions.
• To honor and reflect on Regge's major scientific achievements as part of a commemorative publication by the Accademia delle Scienze di Torino.

Proposed method

• Analytical review of Regge's original 1959 paper on the analytic properties of scattering amplitudes.
• Historical reconstruction of the S-matrix framework as it existed in the late 1950s, emphasizing its role in strong interaction research.
• Examination of how Regge introduced complex angular momentum to describe resonant states and scattering behavior.
• Use of mathematical tools such as analytic continuation and pole structures in the complex plane to model scattering processes.
• Integration of historical and philosophical perspectives to interpret the conceptual shift from perturbative to non-perturbative methods in early hadron physics.
• Comparison of Regge's approach with contemporaneous developments in quantum field theory and elementary particle physics.

Experimental results

Research questions

• RQ1 What motivated Tullio Regge to extend scattering amplitude analysis into the complex plane of energy and angular momentum?
• RQ2 How did Regge's work on poles in the complex angular momentum plane contribute to the S-matrix program in hadron physics?
• RQ3 What was the conceptual and mathematical significance of Regge trajectories in the context of strong interaction theory?
• RQ4 How did Regge's framework influence the development of modern quantum field theory and string theory?
• RQ5 What role did Regge poles play in shaping the understanding of resonances and scattering resonances in high-energy physics?

Key findings

• Regge's introduction of complex angular momentum provided a powerful analytical framework for describing resonant scattering processes in strong interactions.
• The paper establishes that Regge poles emerged as a natural consequence of analyticity and unitarity in the S-matrix program.
• Regge's work laid the foundation for the concept of Regge trajectories, which later became central to dual resonance models and string theory.
• The analytical structure of scattering amplitudes, particularly the location of poles in the complex plane, was shown to encode information about bound states and resonances.
• Regge's approach offered a non-perturbative alternative to Feynman diagram techniques, emphasizing symmetry and analyticity over perturbative expansions.
• The historical context reveals that Regge's insights were initially underappreciated but later recognized as pivotal in the evolution of theoretical particle physics.