Open Loop Amplitudes and Causality to All Orders and Powers from the Loop-Tree Duality.

Area of Science:

• High-energy physics
• Quantum field theory
• Perturbative calculations

Background:

• Multiloop scattering amplitudes are a significant challenge in perturbative quantum field theory.
• Existing methods struggle with the complexity of quantum fluctuations at high energies.

Purpose of the Study:

• To generalize the loop-tree duality method to all orders in the perturbative expansion.
• To develop a novel approach for simplifying multiloop scattering amplitudes.

Main Methods:

• Extension of the loop-tree duality to all orders using a complex Lorentz-covariant prescription.
• Introduction of multiloop topologies with arbitrary internal configurations.
• Derivation of compact, factorizable expressions for open-to-trees representations.

Main Results:

• Development of a generalized loop-tree duality formalism for multiloop amplitudes.
• Obtained expressions are independent of initial momentum flow assignments.
• The new representations are free of noncausal singularities and exhibit manifest causal structures.

Conclusions:

• The generalized loop-tree duality offers a powerful tool for calculating high-energy scattering processes.
• The derived expressions provide enhanced numerical stability and clearer causal structures compared to other methods.