On-Shell Covariance of Quantum Field Theory Amplitudes.

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• High Energy Physics

Background:

• Scattering amplitudes in quantum field theory are invariant under field parametrization, a concept known as coordinate invariance.
• This invariance can be geometrically interpreted using Riemannian curvature tensors, demonstrating covariance under non-derivative field redefinitions.

Purpose of the Study:

• To develop a generalized geometric framework for scattering amplitudes.
• To extend the manifest covariance of amplitudes to all allowed field redefinitions.
• To explore the implications for effective field theories.

Main Methods:

• Formulating amplitudes using Riemannian curvature tensors.
• Developing a generalized geometric framework for field redefinitions.
• Analyzing recursion relations in perturbation theory.
• Investigating 'on-shell covariance' for tree-level amplitudes.

Main Results:

• A generalized geometric framework is presented, extending manifest covariance to all field redefinitions.
• Amplitudes satisfy a recursion relation resembling covariant derivative applications.
• Tree-level amplitudes exhibit 'on-shell covariance' under allowed field redefinitions, up to terms vanishing with constraints.

Conclusions:

• The study establishes a new geometric understanding of scattering amplitudes.
• The framework provides a systematic way to handle field redefinitions in quantum field theory.
• The concept of 'on-shell covariance' has direct applications in effective field theories.