New Representations of the Perturbative S Matrix

Area of Science:

• Quantum Field Theory
• High Energy Physics
• Mathematical Physics

Background:

• The perturbative S matrix is crucial for understanding particle interactions.
• Existing methods face challenges with massless particles and complex loop calculations.

Purpose of the Study:

• To develop a robust framework for representing the perturbative S matrix.
• To ensure the framework is well-defined for all quantum field theories involving massless particles.

Main Methods:

• Constructing the S matrix representation from tree-level amplitudes.
• Utilizing integrable terms and partial fraction identities from Feynman diagrams.
• Defining loop integrands using "Q-cuts" with specific contour prescriptions.

Main Results:

• The proposed framework is well-defined for massless quantum field theories.
• It simplifies loop integrand evaluation using Q-cuts.
• The framework naturally extends to all orders, including nonplanar theories.

Conclusions:

• This new framework offers a unified and systematic approach to S matrix calculations.
• It provides a powerful tool for theoretical physics research, particularly in quantum field theory.
• The method has implications for understanding scattering amplitudes and quantum gravity.